My present computer has exactly that VPU, a Radeon 9800Pro with 128MB memory. My processor is a P4 Northwood at 3.0Ghz and 800mhz fsb on socket 478. Not a bomb, but good enough compare to the Prescott that followed it.
I played Far Cry at 1280*1024 without any problem with setting at medium or good (out of low, medium and good, + ultra for water). I was getting a bit over 30 fps if I'm right and never got scene missing or skipping. Half-Life 2 is exactly the same (1280/1024 with medium setting) and sometime 1024*768 but with more "effects" on. I didn't play Quake 4 tough.
You should know that more recent games like Oblivion and/or FEAR will force you to reduce both resolutions and quality setting to get playable fps (frame per seconds). But it doesn't look to be considered anyway. So I'm just mentionning it.
You should remember in your case (no offence I hope) that your Athlon 1600+ will also be a limiting factor. So putting anything more powerful will be limited by your cpu in most case. So a 9800Pro is really the sweet spot I'd say for your cpu, as long as you don't mind not having all eye-candy maxed-out.
Forget about the GeForce 5900, it was NVidia worst VPU in their whole history. Any of NVidia 6600 (or more) VPU for the same price would also be a good choice, if not better for games using pixel shadder 3.0 not supported by the 9800Pro. I wouldn't base my choice on this, since game needing it usually need really powerful VPU, but you should know. Still, the 9800Pro is the best choice I think.
Good luck and happy gaming!