As mentioned, quality running shoes are key. Beyond that, it depends on the conditions where you are. Cotton fabrics are typically to be avoided because once they get wet (sweaty) they can chafe and just weigh you down. Choose technical fabrics that breathe and will wick the sweat away from your skin. Whether to wear leggings, capris, or shorts, a tank top or t'shirt style top (or go topless) is your call. Also, get socks that aren't cotton (you don't want blisters). Wear something that is comfortable and you can move in (you don't want to feel like it's too binding or that it's so loose and floppy it bugs you.
Notice the people in your area who run, and look at what they're wearing. Your local running store will have a lot of options and even if those things aren't in your budget, you'll get an idea of what to select from at a store that may be more affordable (even discount department stores often have working/running attire).