Those are my system spec's although I only have 2 drives. The 6600 is okay but if you expect to keep this system longer, and depending on what you do with it (heavy gaming, movies, email, etc.) you should also consider 7600GT or a 6800GS if you can find one. Maybe a X1650. Could try and then just upgrade your power supply if needed. Unless you are trying to avoid putting much money into that system. I think the 6600 will run on your 350w but only a test will tell. I have a X1600 but also a 500w PSU.
i agree with PMR on this one, the 6600GT is far better than a 6600.
the 6600GT is 500/900 and a 6600 is only 350/700?
i had a 6600GT and they are great cards, and you have a couple of choices in this range. 7600GS, 6800GS, 6600GT, x800x, x850x. id go with one of those but your PSU is a lil low for all the hardware you have.
6600GT is a reasonable match for that system. Some would argue XT800GTO which is faster, but others like nVidia's drivers better and frankly, on an aging system such as that, the difference will be minor at most.
Likewise, buying any higher performance card at higher cost will probably be a bad purchase unless used on a very high resolution display. To spend a lot more it would be wiser to upgrade the motherboard to PCI Express first and replace what will be the bottleneck with even the 6600GT- the XP2500 CPU.
Your motherboard uses 5V for CPU power, leaving most of the 12V amps unused but for 2-3 to spin up the drives when the system is powered on and a trivial addt'l amount for fans. You are in a better position to run a 6600GT or similar with a 350W PSU than someone with an otherwise identical system but CPU VRM supplied from 12V rail. There is no guarantee it'll work for years and years like that, as it is a medium quality PSU and not a "Lot" of reserve power after this upgrade, but in general it should work.