If you get wool, make sure it's not "washable wool"- that kind has been treated to make it "easier to wash" but it also ruins the water-resistant properties that make it such a great material for diaper covers. Wool works beautifully for diaper covers (as long as it's not treated for washability). Acrylic works fairly well too. A wool/acrylic blend will work- the higher the wool content, the better. A wool/cotton blend wont' work so well- you'll get a lot of wicking.
I'm not sure about specific brands of wool or needle size. Your best bet is to ask a salesperson for help, find the appropriate yarn, and then buy needles that work well with that thickness of yarn. I also suggest buying a few sizes of needles- you may want to size up or down from the "recomended" size for that yarn, depending on whether you work tightly or loosely.