7600GS or 7600GT, depending if you have something better to do with the ca 50$ more 7600gt costs. Personally i dont think there is a point in pumping so much money in such an old system, so i would go with 7600gs.
The fastest card you can get is probably limited by your PSU. Please post specifications - make & model and power output (the latter should be on a label on the PSU or available from the manufacturer online). Does it have an available PCIe power connector (so named but also used for higher end AGP cards) and/or two available 4 pin molex connectors?
Because the FX5600 is a power hungry card (65W) you should be able to go with most other current options - including the 7600GT (36W) or either the 7900 GS (45W) or x1950Pro (66W). Depending on how close you are to capacity on current PSU, you may need to consider that PSU efficiency decreases a small amount over time.
The 7900 GS and x1950Pro are approximately equal in speed with an edge to the x1950Pro but the 7900 GS overclocks better and the x1950Pro takes a lot more power. Both are about 50% faster than the 7600 GT.
For most games, your CPU is a minor consideration, but perhaps someone with your CPU and one of the faster cards can tell you if there really is any performance loss - or what specific games might be affected.
I have in what is now a htpc rig a athlon xp 2500+ oc'ed to 3200+ a palit 7600gs with ddr3 i oc'ed it to 550 core and 1250memory and i played test drive unlimited on high, oblivion with low to medium setting with no lag and bioshock with high details.
The 7600GT will be quite a bit better than the 7600GS.
However, either will be a huge improvement.
Much depends on your finances and how long you plan to your very old system. Any thing you spend on the card will be lost when you upgrade the rest of your system.
Yeah, I went from a 5200 to a 7600GS and I used a 3D benchmark that was a flyover some trees (I think it was part of PC Wizard or something). Anyway, it went from a barely veiwable slide show (maybe 8-10 FPS) to smooth as butter (62 FPS). I think the 6-8x increase in processing power was more than enough.
I had a somewhat similar set up.... a P4 2.53 GHZ system w/2gigs of PC3200 ddr on a Soyo P4x400 board. Original vid card was 9800pro.....great card in it's time.
When I updgraded to a 7800GS graphics card, I found it was considerably better - but not to the tune of what I'd hoped for after studying a lot of benchies. I put a x1950 pro in the same setup to find that performance had only marginally improved. Major bottlenecking seemed to be the problem. (cpu, bus, etc.)
Swapped out the motherboard and CPU and almost doubled my performance from the x1950pro.
It's worth the time and money just to upgrade the platform.