I'm not totally sure what you want; Do you want to build a PC yourself, or do you want to buy a whole pre configured one like those from Dell.

I can't really think of building a PC for under $350 that is even decent. You'd be better off buying a Dell, or an MDG.

You'd be kinda off like this

CPU: <>50 (I'd get an Intel Dual Core Celeron or Pentium Dual Core and overclock) [I'd go with a 775, cause you can go quads when you think this is getting old.
Motherboard: <>70 (Depends)
Ram: $30 (2x1GB DDR2-667) Higher the better for overclocking (I got OCZ PlatXTC 800 for $20)
HD: $50 (depends)
Case (w/ PSU): $50 (depends)
CD/DVD drive: $30 (Depends)
Video Card: $30 (6200, 7300, 8300 or other lower end, mainstream[6200, 8300 or 7300, you can attempt to flash a mid end x600 series BIOS (6200 -> 6600, 7300 ->7600 8300 ->8600 (OWN RISK, i never tried before)) For a little more, you may get a 8600GTXXX which can run CS: Source over 150 FPS (regardless CS 1.6). I have a 7600GT that runs over 160 FPS with some hogging anti virus program.

-> $310; Doesn't include monitor, nor keyboard, mouse, or taxes.

I have a compaq AMD pC that will play WOW, CS and CS source. $200 has 60 gig hd and 1.5 gig mem nvidia 5500 256 mem video card.

build your own with AMD 780g on board graphics. if you've got an old system to scalvage parts from.

figure a MoBo, CPU and memory for $200. If youve already got a case, PSU, HDD and OS, your good to go.

then down the line you can upgrade graphics and add in a quad core and whatever else