How familiar are you with computers and their hardware? Do you want to build a new PC, buy a new PC, or replacing components on an existing one? $600 for a "gaming" PC is a bit low, although if it is just for casual/lighter gaming that's doable. Many things to consider.
If you plan on replacing parts or building a computer you should do plenty of research and learn as much as possible before you build; same with replacing parts yourself. buying a new one requires you to have some knowledge but less than building.