Does it matter what kind I buy?
Yes, it matters what *kind* you buy, but it doesn't really matter which brand-- just whichever one is easier for you to work with. Make sure it's bakeable clay and not modeling clay. It WILL melt in the oven (For example, using non-bakeable modeling clay as a filler for larger sculptures may or may not result in said sculpture cracking/exploding and oozing hot, melted slime.
Not that I'd know that from first-hand experience or anything. Nonetheless, you have been warned). Some polymer clay brands are Fimo, Sculpey, Premo (I believe this is made by Sculpey), and Kato.
What's the difference between the different brands?
FIMO SoftSoft, and sturdier when baked because it stays slightly flexible. The darker colors will stain your hands, but this can be washed off easily with some good dish-soap. Non-toxic.
FIMO ClassicBasically the same as FIMO Soft, but it's harder. Go figure. Non-toxic.