Actually, an A64 3000+ and a gig of RAM is a pretty decent setup. And, hell, I got FarCry running on a 1.4GHz Athlon T-Bird and a GeForce2, so no sweat there. Quake4 will be a bit of a stretch, but I would hope that it will run on low settings at least.
The only blatant weakness in your system is the Graphics card, and that isn't *awful.* I would try to upgrade to a 6600 ($), a 6800GT ($$$), or a 7800 (!!!). Probably an AGP slot, so the latter is out of the question.
To be honest, I'd get a PCIe mainboard along wiht a 6800 or 7800. Since you are running an A64 already, any Socket 939 board will do. Just get an ABIT or ASUS brand board to save yourself the hassle or motherboard replacement...most other brands aren't worth the bother. A8N series from ASUS is the best in field.
If you're talking serious money, get the A8N SLi, which gives you a pair of PCIe slots, allowing you to expand to a pair of graphics cards in an SLi configuration (in the good old days, it was called Scan Line Interleave...not sure what it means these days).
I'd actually wait on the graphics card, watch prices. The ATI X1000 series just came out, and hopefully that'll drive down NVidia's prices.
In the future, another gig of ram (These days, arond $100 or so) wouldn't hurt. I assume you have some open slots for RAM still.