What will I need/want in terms of equipment?

You will need the following:

• * A DSLR. It doesn't matter what make or how many megapixels. Obviously the newer ones have more pixels and more features. Live View is quite handy but by no means essential. 5mp or more is good. I currently use an Olympus E330, though literally any modern DSLR will do a capable job.
• A bellows unit which either fits you camera directly, or with the use of an adapter. Personally I use an old OM Auto bellows with a "Olympus MF1" 4/3 to OM adapter.
• A lens which fits on the front of your bellows. I use an Olympus OM 50/1.8 lens for larger bugs - wasps, bees, butterflies, damselflies etc. So a standard MF 50mm lens for you camera mount of choice is a good place to start. You can move onto more specialised higher magnification lenses later!
• Lighting of some sort. If you can afford it then a macro twinflash does a good job and is also useful for outdoor work with live bugs. For indoor studio stacking a fibre optic illuminator for a microscope will also work well, either with twin light pipes or a ring light attachment. Other cheaper options are a single off camera flash, or you can just use a desk lamp or two (Just watch the heat!).

* Note you can do this kind of stuff with a Point and Shoot camera but you cannot use a bellows unless you can remove the lens. So using a Point and shoot means using additional lenses (diopters) on the front of the cameras built in lens, which can reduce image quality.

You will definitely want the following:

• Some sort of focussing stage. The OM bellows includes a focussing rail, but this is really only good for magnification up to around 2-4:1, beyond this the smallest movement you can make is not small enough for the focus steps you need, and the alignment is not perfect which can cause issues. At the moment I use an Aerotech linear stage, and until recently used a "Prior Micromanipulator" to move the specimen relative to the camera. Another option is a Mill table. Another option for a vertical rig particularly is the base of an old but decent microscope. (Seethis thread for some good info on this subject)
• A base of some kind, a piece of hardwood or metal very roughly 15 inches by 20 inches (by at least 1/2 to 1 inch thick. A bit larger would not hurt, a bit smaller may or may not depending on the size of your bellows and subject mount.

I started out without these components, with the bellows/camera/lens mounted on a sturdy tripod, and the subject placed on a pile of stuff to bring it in front of the lens (and using the OM bellows focus rail to move the camera to adjust the plane of focus). This is not really a satisfactory setup but you can do some lower magnification (up to say 2:1 or 3:1) test stacks like this if you haven't got around to setting up a proper fixed rig.

These will probably also be useful:

• Small modelling paintbrush for cleaning specimens.
• Air duster for cleaning specimens.
• Diffusion material of some sort: Tissue paper, ping pong balls, plastic tubs are examples of stuff you may have lying around which you can use to diffuse light. Or you can spend more money on proper photographic lighting diffusers.
• Low power stereo microscope for inspecting and cleaning specimens.
• Insect net and specimen containers.
• A Fridge-Freezer. (To kill and store the bugs).