Alright, I built my current system with 600 dollars. Its a great system (just have a few kinks to work out with heat management, because of some rather annoying little quirks in my build, but nothing horrible)
I'm basically running what most people would call "crap", but I'm a solid believer that old technology is good technology, because not only is what I got very cheap, it has lasted me pretty well with any of the newer games.
I know you want AMD, but lets just show you what I ended up getting.
Intel Pentium 4 3.20E Ghz Prescott 478Pin, 1Mb L2 Cache HT enabled
Asus P4P800S-X
1Gb (2x512) GeIL Valu-RAM (can run dual channel, however, my current motherboard, which I did not notice, doesn't support Dual channel
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ThermalTake Tsunami Dream Aluminum case (great case, very light, very well made, has some awesome reviews as well, but its rather spendy in a 600 budget)
120Gb WesternDigital 7200RPM HDD SATA
I didn't get a video card at the time, because my 5600 Ultra was still going strong, till it decided it was done, and cooked itself. I now have a eVGA 6600GT 128mb AGP8X. Its awesome. Chances are, unless you cut back largely in other areas, you won't get a damn fine CPU as well as a GPU. You have to cut in one or the other, because a good CPU is gonna run you 200+, usually 250. Same idea if you want a good GPU. Thats 300 dollars gone already, if you got an eVGA 6600GT, but then you've still gotta get your case, RAM, and new HDD (go SATA) and RAM alone will likely run you 100+, so will a HardDrive. You still haven't gotten your mobo, which is gonna run you 60+ for a good one, as well as the case price not being factored in.
Don't sweat it though, the people here will get you the good stuff. These guys know their shit, just trust em.
I'm just giving you MY point of view, cause I'm a cheap bastard, and won't spend more than I have to. lol