Work in progress - this is more of a placeholder at present.
Equipment Checklist
Air Compressor: You will want an air compressor with a decent SCFM (Standard Cubic Feet per Minute) rating, preferably with a 100% duty cycle. You can also get creative and gang multiple lower-end compressors together, but it's easier just to buy a higher-end compressor to begin with. It is nearly always the case that you can get a used commercial-grade compressor off of Craigslist for less money than the smallest compressor you might want to use for this at a shop.
Blasting Apparatus: This may be a blasting cabinet, or it may be just a nozzle and a media collector. Either one will work, just know what you're using.
Blasting Media: Depending on what you're trying to do, you may prefer aluminum oxide, sand, glass beads, steel shot, or carbide.
Inline Water Removal System: Wet air leaves your media clumping; dry air works best. A properly set up inline water filter will condense the moisture out of the air you're working with, so that the air you use for blasting is dry.
Safety gear: This is both respiratory and eye protection. In some cases (full helmet, supplied air system) this may be one piece of equipment. Please read the Respiratory Safety article for more details. This is a very important topic.
Respiratory Protection
Respiratory safety is treated in its own topic - this is only a small piece relevant to abrasive blasting
Abrasive blasting can be one of the most unhealthy things in gunsmithing. Even with a good blasting system, you're likely to produce a lot of fine airborne particles. Depending on what you use for media, you may be at serious risk for silicosis. If you choose to use sand as a blasting media, the utmost caution must be exercised to avoid silicosis - which is an irreversible respiratory condition commonly found amongst sand blasters. The easiest way to avoid this is not to use sand or glass bead media - aluminum oxide doesn't cause silicosis, and it's a readily available blasting media. Glass bead media is a risk because the glass beads frequently crack when they strike the work piece, into smaller and smaller fragments which eventually get small enough to cause silicosis.
If you are determined to use sand, don't just figure that a wet rag wrapped around your face or a painter's filtration mask is adequate protection! Consult the fine print on any respirator you're considering using for this. The VAST majority you can find in a store say, on their filters, "not for sandblasting". Crystalline silica particles will generally make their way through most protection methods you may use.
After long and (admittedly paranoid) analysis of the costs and benefit, I chose to go with a supplied air system. Your mileage may vary.
-- SeanNewton - 07 Jan 2012