I would get a set; it's infinitely more satisfying when your underwear matches. That could include knickers + bra + garter belt or bra + corselette + thong or just a bra and bottom, whatever it is that you use. If you're really OCD you might want to get a matching nightslip/nightgown too. It's fun to prance around the house in that.
Look for the bra first (and try it on) because finding a good fitting bra is harder than finding knickers, so once you've found it you can just get the matching bottom. A black or nude set is probably a good place to start. Black goes with everything, shows less wear than white does and it looks fine under sheer clothes, whereas nude is good to wear under white clothing and if it's lacy it can look quite pretty.
Double-check that it's comfortable, practical and that you can actually wear it under clothes (if that is what you're gonna do with it).
Once you have a set or two, I think every girl also needs a nude strapless bra (although I often don't wear anything under strapless dresses) and one that gives huge cleavage and is as exotic as possible!