When I used the gym (!), I wore comfy cotton shorts, sports bra, t-shirt (or sometimes spaghetti-strap tank top) with typical tennis shoes. Nothing fancy, just comfortable.
A bit random, but for some reason I've observed here in the UK that girls tend to wear NORMAL BRAS a lot when jogging/working out. Yes, the serious runners still wear sports bras, but I seriously see women all the time and it's quite clear they are wearing a normal, wired bra. Why on earth would you torture yourself like that?! Has anyone else noticed this, or am I just crazy?