There are 2 basic types of dyes: Fiber Reactive, which is used on cellulose (ie: plant) fibers, and Acid, which is used on protein (ie: animal) fibers. (I'll hit on so-called "natural dyes" later.) This is basic - you *can* dye wool with FR dyes, but the color won't be as strong, and may not be as washfast - but generally speaking, you choose which type of dye by what the item is you're dyeing. I have virtually no experience with FR dyes, since most of my mad scientist forays have been with wool, using Jacquard brand dye. So, my info on FR dyes might not be perfect, but for this discussion, that's pretty much OK.
FR dyes use soda ash to permanently fix them to the fiber, Acid dyes use, well, acid - the home versions generally use good ol' cheap, easily available vinegar. You can also use Kool-Aid on wool, and food coloring - from what I understand, the chemicals in both are the same as what's in the Jacquard/Home type dyes (but maybe there's more in them as opposed to the Kool-Aid? Not sure - but I don't serve Kool-Aid to my kids anymore!)
Then, there's a whole 'nother subset of dyes: Union Dyes. Rit is one. Basically, a union dye has color for *both* types of fiber - if you're dyeing protein fibers, the Acid dye hits, and the FR dye washes down the drain, and vice-versa for the cellulose fibers. Yes, it is a bit wasteful (you're running 1/2 the dye package down the drain), BUT - if you are only doing a one-off dye job, it's cheaper to use Rit, since you can get it NOW, and get it at pretty much any grocery store. The major problem I have with Rit is the crocking - a lot of loose dye will run off the item for the next 2 or 3 washes. Not a big deal - just make sure you wash the item by itself or with something you don't mind getting tinted.
If you're doing production dyeing - say you're making a bunch of stuff to sell - then Rit is Not the best thing to use. You can't really guarantee color matches from batch to batch (sometimes all the dye will strike at once, sometimes not - adding salt to the dyebath helps a little), and it gets cost prohibitive over time. In that case, buying the "real" dye (ie: Procion (FR) or Jacquard (A)) would be more economical.
Now to touch on the environmental safety issue: Rit's probably not the safest stuff to use, since you're washing 1/2 of it down the drain. Again, for the normal home dyer, this isn't *that* big of an issue - how often do you actually dye?. When I do a batch of wool, it's usually 1 pound at a time, using 1 Tbs of dye powder and a good glug or 2 of vinegar. Most of the dye exhausts (except for Turquoise and Teal - those 2 colors have never fully exhausted (completly bind to the fiber) for me.), so all that's theorectially in the water is a little bit of vinegar (and maybe salt) when I dump it. FR dyes work the same way - just the residue of soda ash is left. Again, not a whole lotta stuff going down the drain.
So-called "natural dyes" are a whole 'nother ballgame. They use natural stuff - wood chips, nut hulls, flowers - for the color, and use stronger chemicals (alum, tin, iron, etc) to bind the color to the fiber. (They're called mordants). I have a sneaking suspiscion that they are no better for the enviornment than the commercial dyes.....but haven't run any tests. With 2 kids, I don't feel comfortable with the mordants lying around, so I don't play with natural dyes much. Yes, they've been in use much longer....but that doesn't make them better. (I do love some of the colors you can get with natural dyes - I'm not knocking natural dyers here! I just like the predictable results I can get with "chemical" dyes, and the ease and fast set up.) I'm not sure what the leftover mordants would do to a septic system over time.......of course, I'm not sure what vinegar will do to my system, either! You don't use a whole lot of the mordant, so the question may be moot.
ANYWAY, back to my point: Rit dye is great for the occasional home dyer. It's relatively cheap (for small batches), it's available, and it's easy to use. If you're gong to get into a more commercial bent, spring for the "real" dyes - but that doesn't affect most of us "normal" people.
It's early, so I probably left out a bunch of stuff I wanted to include. *sigh* Feel free to ask questions/tell me I'm an idiot/whatever. *g*