The first and foremost question you have to answer is: what is your budget? To give you an idea of what a particular price segment will get you (these are not including the OS, tack on $100 extra)
- $500-$600: Bare basics for a gaming computer. It will play most games made within the last few years at 720p on high detail just fine (30FPS-40FPS) with titles older than that running smoother or you can push the resolution up a bit.
- $600-$700: Most games made in the last few years can be played at 1680x1050 on high detail smoothly (50FPS or so). Older titles you can certainly run at 1080p at high details or better without problem.
- $800-$1000: You can start pushing the envelope to 1680x1050 or 1080p on maximum detail and it'll hit 60FPS or higher most of the time. Demanding titles may run 60FPS when nothing's going on but may dip down to 40FPS or so when the action picks up.
- $1000-$1200: Most games at 1080p on maximum run smooth. Demanding titles will have occasional dips.
- $1200+: You can pretty much play any game at 1080p on maximum detail at 60FPS constantly. Most games will even run smooth at 2560x1440 or 2560x1600.
Most of the budget should be weighted towards the GPU.