I have
Intel Pentium 4.0 3.0 GHZ w/ Hyper-Threading (Intel sucks, get AMD it scores higher on CPU Mark overall, less heating problems)
NVIDIA GeForce 7800 GS (AGP) w/ 256 MB of vRAM (PCI-E is better, but not necessary if you don't want to spend as much and have an AGP slot on your mobo)
1 GB (512x2) RAM, Dual-Channel
500 Watt PSU
I run games like Oblivion on 1024x768 w/ highest graphic settings, AA and all, and at a good FPS rate. Anyone who says you need 2 GB or more of RAM is retarded; you don't need it, but it helps.
I'd also recommend good cooling... don't want any parts working themselves too hard now :D!
I didn't spend much more than say $1600 (CDN) on my comp, and that's with all that I mentioned plus a 160 GB SATA HDD, a 300 GB SATA HDD, optical drives are cheap so that's not as important, and audio cards I don't give a **** about so I'll go with on-board.
Basically, I'd recommend AMD for a CPU, and frankly go with ATI or NVIDIA on video cards, they're both pretty equal for the most part. Some ATI cards score higher FPS rates on newer 3D Mark/High-End Games, but overall NVIDIA cards seem to hold out longer. Hell, I was still running Oblivion on an old GeForce FX 5700 for a while, till I upgraded.
Expect to pay a bit more than $1200, but you should be able to get a pretty high-end desktop PC for that price.
P.S. - Windows Vista = Gay, uses video card. That = Useless, it has no reason to use up more power. Don't get Vista, it'll just be a waste of CPU power and RAM.