There’s tons of builds around the internet that range from budget to what normal people can afford (yay for those builds, lol) to high end; search around sites like MaximumPC, Tested, etc., and see what kind of stuff they recommend. You’ll also find forums dedicated to building rigs and lots of people there will post benchmarks of their rig to let you get a feeling for what kind of frames you’ll be getting.
I built my PC for $600 a couple years ago (e8400, XFX 4870, 4gb of ram, and a gigabyte ep-45 ud3l mobo if I recall right) and it’s ran well with only one major-ish problem (64 bit Windows 7 caused a major sound stutter on games for some reason, but dropping down to 32 bit fixed it and it didn’t really hurt my performance).
NewEgg is probably the best site when it comes to buying parts. I’ve used TigerDirect and Xoxide for stuff, but I just prefer NewEgg. Everything comes quickly, they have good deals, and most people have had good interactions if something does go wrong.
By the way, PS3’s aren’t cheaper when you factor in the games. Think about it. I paid $600 for my PC, you paid $300 for your console. You have to buy new games at 60$, while I can wait just a couple days/weeks and buy mine for $30 or less on Steam. I could also wait half a year and get it during a major Steam sale and pay like $5 or buy a pack of like 10 games for $20, while your game would still be at $60. See how easy it would be for you to pay way, way more than that extra $300 it costs me to build my rig? We’d be on even ground then, and I’d still be saving money every time a game came out.
Consoles aren’t better for the FPS genre at all. A good analogy for this would be having to drive a nail into a piece of wood. A mouse is like a hammer, while a controller is more like a brick. Both can pound things, but the hammer is made for the job, while the brick isn’t. Controllers have their place for sure (fighting, racing, etc), but FPS is really a job for a mouse. It appears easier because you think “oh I can just move it to where I want it,” but when you’re actually playing you’ll realize it isn’t just point and click.