Enough disclaimer. On to the real stuff...
Power tools for carving can be broken down into two major classes: air driven (pneumatic) and electric. Common pneumatic tools for stone carving include:
Air hammers don't actually look anything like a hammer. There are two kinds that I know of -- big ones for demolition work and small ones used for carving. The demolition hammers are generally shaped like pistols and their chisels lock in place. Carving hammers are shaped like a barrel -- the air hose connects at one end and a chisel slips into the other end without locking. In both cases, the incoming air causes a cylinder or piston to move back and forth inside the tool, hitting the chisel and driving it into whatever is being worked.
The piston moves many times a second, but it doesn't move far. My hammer has a total movement of less than one inch. The effectiveness of the air hammer doesn't come from the weight of the piston or the force of each blow, but rather from the huge number of blows given to the chisel in a short period of time. Soft stones crumble before it, and they almost always break in a nice, simple, and predictable manner.
Stone carving air hammers come in numerous sizes, from small -- nearly pencil sized -- up to something larger than my hands will comfortably hold, and I'm 5 feet 11 inches tall. The size of the hammer itself changes the size and weight of the piston as well as the distance it moves, so larger hammers hit the chisel harder. The chisels you use must fit the hammer you have. Adapters will let you use smaller chisels in a larger hammer, though I have not personally tried this.
Chisels for an air hammer are different from those used with hand tools. First, they are round on the end that goes into the air hammer. If you pick up a chisel that is hexagonal in the middle and round on the end opposite the point, teeth, or flat, then you're almost certainly holding a chisel for an air hammer. Secondly, they are tempered differently. Chisels for air hammers have to be hardened on both ends. The end that goes into the air hammer must not "mushroom." That is, it may not bend out and deform in response to the blows from the piston in the hammer. If it did, it would scar up the tool, and possibly damage the piston and cylinder walls when bits of metal break off the tool. Hand chisels aren't tempered except at the business end. If you look at your old hand chisels you'll see some mushrooming on them somewhere, I'm sure. (Safety tip -- grind or file off that mushroomed metal on your hand chisels. It gets sharp and can break off hitting someone in the eye or lurking on the floor to be stepped on later.)
Given all that, when you buy an air hammer, you also need a new set of chisels to use with it. Keep them separate from your hand chisels so you don't use one with a hand hammer by accident. You'll need to experiment with your air hammer chisels on the stones you carve to figure out what you like and want to use. As with carving by hand, the rule is to figure out what works for you, rather than to follow the rules.
Personally I have a Cuturi "V" size air hammer, and I am very happy with it. It takes chisels with a half inch shank -- a common size -- and provides 6500 blows per minute according to one catalog I have. It needs about 5 CFM (cubic feet per minute) if air at 70 PSI. (I had to do the math to translate those units out of Metric and into English units. It uses 140 liters of air per minute at 5 atmospheres, I think. I don't read Italian all that well.) They are imported from Italy and are quite nice. You can also buy an American made air hammer from a company called Trow & Holden. I've never tried the latter, but I know professional carvers who love them, so I suspect they are excellent tools as well.
When using an air hammer, there is generally a maximum upper pressure that the manufacturer specifies -- 70 PSI in the case of my Cuturi hammer -- but lower pressure can sometimes be useful. Turning down the pressure reduces the number of blows and the force behind each blow. When you are trying to carve more gently and don't have a smaller air hammer to change to, this can help. It isn't the perfect answer, and I always switch to hand tools when I get close to my final form, but it can help.
A final note about air hammers. It is possible to get certain kinds of repetitive stress injuries while using them. They vibrate while used and that can cause all kinds of problems. I strongly recommend you wear a set of anti-vibration gloves while carving with power tools, but particularly when using an air hammer. If you don't, you'll probably fill a tingle in your hands for some time after you stop, and that will turn into permanent damage over time. I like full finger anti-vibration gloves, but fingerless gloves are common and many sculptors prefer them.
Die grinders are simple tools that have a collet and nut at one end that lets you insert and lock down any number of grinding or cutting bits and burrs. Die grinders spin at high speeds -- often up to 25,000 RPM -- and can thus move a fair amount of stone quickly if you have a good burr in them.
A simple die grinder is perhaps 5 inches long and 2 inches or so in diameter. Air comes in at one end and the burr is secured in the opposite end. A long switch along the side allows air into the grinder, spinning the burr. Release the switch and the burr stops spinning. Most die grinders sold in the US accept burrs with a 1/4 inch shank. I don't know what happens in smarter places that have gone totally to the metric system.
You can find several variations on die grinders. Some rotate the collet and locking sleeve/nut 90 degrees. These are called angle die grinders. They work exactly like a standard die grinder, but may allow you to get the burr into some places more comfortably. Other die grinders have long necks, moving the burr 5 inches or more away from the part of the tool you hold in your hand. These allow you to get the burr deeper into your sculpture.
Die grinders use differing amounts of air, and are made by a fair number of manufacturers. I have two from Home Depot under the Husky brand name. One is a standard die grinder, the other is an angle die grinder. They're good, basic tools, work fine, and didn't cost a fortune. I also have a Dotco die grinder with a long nose. This is a very nice tool, but it uses a LOT of air and cost a lot of money. Many die grinders will use 4-5 CFM at 90 PSI. My Dotco grinder uses 13 CFM at 90 PSI. It isn't possible to drive my Dotco grinder from most portable compressors as a result of the amount of air it consumes.
You'll find grinding burrs in all kinds of places. Any hardware store that carries air tools will probably have some grinding burrs. I prefer structured carbide burrs to just about anything else. Anything metal with actual teeth will work in very soft stone but will go dull quickly thanks to the heat generated by the grinding process. Structured carbide lasts longer and works on harder stones.
In general, I suggest you buy a die grinder and some burrs only when you find yourself working on a carving and thinking it would help. Buying them in advance is fine, but you may discover that your pieces don't require one right away. If you work very large they may not be required at all, and if you work small you're probably better off getting a flexible shaft tool rather than a die grinder.
Also note that there are electric die grinders available. I don't recommend them much, though. They are heavy -- several pounds -- and much larger than the corresponding pneumatic tool. For some reason they also seem extra susceptible to vibration damage to the housing. (I've repaired one for a student of mine several times. The problems have been cracked plastic bits in the housing, pinched wires, damaged insulation, and a sticky switch.) I'm sure that stone dust isn't good for the motor either, and these need a lot of air to keep them cool. If you have a compressor, stick with a pneumatic die grinder.
A first note: you almost certainly want an electric angle grinder. I have seen -- and even own -- a pneumatic angle grinder, but they just aren't as versatile as the electric ones. Many companies make electric angle grinders, including all the big tool manufacturers, so you have lot of choices if you go looking around.
What is an angle grinder? Well, simply, it is an electric motor that spins a disk. You hold it in such a way that you can lay the side of the disk down on the stone you are carving, or you can push the edge of the disk into the stone. There are many kinds of grinding and cutting wheels that can be used. I'll try to describe some of them below. It is also important to note that angle grinders come in a variety of sizes, based on the size of the disk they spin. You'll find at least 4, 4.5, 5, 7, and 9 inch versions. The larger tools are heavier, and probably more useful for large works. I recommend a 4.5 or 5 inch model for most work.
What can you do with an angle grinder? Well, with a good abrasive disk installed you can quickly and easily shape stone as you would with a file or rasp. However, it moves stone much more quickly, and can let you get to a finished shape amazingly fast. Also, with the installation of a diamond blade, you can cut slots into the stone. If you cut several parallel slots half an inch apart or so, you can come back with a hammer and chisel and knock out the material between the slots quickly and easily. Obviously if just cutting the stone to the depth that your blade and grinder allow is useful, you can do that too.
It is important to note that an angle grinder minimizes the stress applied to the stone. If you're carving a piece of alabaster full of fissures and are afraid it will fall apart under a hammer blow, an angle grinder won't stress it much at all. It is possible to get some amazing carving done in very short order with an angle grinder.
Whose angle grinder should you buy? Every major manufacturer makes an entire angle grinder line, and you can spend as little or as much as you want. There are at least two schools of thought on that, and they both have some merit:
First, most of the things you are going to do with your drill won't throw a lot of dust around, so that isn't too much of a concern here. However, you may run the drill for prolonged periods, and may be drilling into hard stone. That means a good quality drill is probably in order. A cordless drill -- while very useful around the house -- is not going to be useful for stone carving. Get a good, powerful, corded drill. Unless you plan on working on super huge pieces, a standard 3/8 inch chuck is just fine.
What will you actually do with your drill? Drill holes, obviously. The most common case is drilling holes for mounting pins and attaching sculptures to bases. However, there are other cases where you will drill one or more holes into a piece for other reasons. Sometimes they may be guides for other tools; sometimes they may actually be used to remove -- or nearly remove -- stone. (Imagine drilling a series of wholes all the way through a stone, close together, in a circular pattern. When you are done the middle section is going to be very easy to remove with a hammer and some fine chisels, right?)
You'll need a selection of masonry drill bits to go with your drill. I get these from the hardware store as I need them, since my needs vary. At this point I own over a dozen in different diameters and lengths. It is a good idea to have a basic set, though, to drill holes for mounting sculptures. I start with the smallest drill I can get and work up to the size of the threaded rod I am using to mount the piece.
Another thing I use my drill for is countersinking the hole in the bottom of the base so the nut and washer I use to attach the sculpture to the base aren't visible and won't scratch anything. For this I need some masonry and/or wood bits -- depending on what material my base is made of -- in sizes all the way up to 1 inch or so. This isn't a perfect way to create a countersink since the bottom of the countersink itself isn't flat (at least, not with a masonry bit) , but it's good enough for the work I do.
If you are carving anything harder than marble you're heading into territory that I know nothing about. Hammer drills and the corresponding hardened bits may be a good idea for you, but the rest of us can skip them. A regular drill and standard masonry bits have worked fine for me so far.
I use chisels as my wedges, though I am sure that specialized stone splitting wedges are available from someone -- probably some Italians living near Carrara. That leaves the question of what is used to cut the initial slot into the stone. There are at least two choices.
Interestingly, cutoff saws can be gas or electrically powered. A large gas powered cutoff saw can cost well over $1000, so it is basically a luxury item I have never considered purchasing. Electrics can be found for less, but I have yet to find one for enough less to cause me to buy it. (The last one I saw was about $800.) Diamond blades are available as well -- at a high price -- if you want them. They certainly aren't needed for alabaster and similar soft stones, but they are useful for marble.
The big names in flexible shaft tools -- also called moto-tools -- are Foredom and Dremel, but there are many imitators, some of which may have legitimate claims to being better than the major brands. You can find models from very cheap to very expensive, so you'll want to shop around.
There are literally hundreds of different grinding burrs, cutoff wheels, and other items that can be used with a flexible shaft tool. Diamond burrs in a variety of shapes are useful for detailed carving, particularly if you are working realistic figures and the like. Abrasive burrs in many non-diamond varieties are also available. Consult the documentation at the store you're buying from on what they are good for. Structured carbide burrs are available in small shafts for these tools, and I like them.
One of the simple things these tools can be used for is to sign your work. A thin diamond burr can engrave your signature into just about any stone.
As with many of these power tools, I suggest buying one only when you decide it might be useful. If you always work large or abstract with few details you may never need a flexible shaft tool.