The best card for your money would be a 560 ti. You can find some of them on newegg for $220 with a $20 rebate. This card will perform much better than a non ti 560 for only $10 more after the rebate.
If you need it to be under the $200 then a 560 would also be a good choice but keep in mind that it will not give you the same performance as the ti version will, it is basically just a 460 that runs cooler.
That CPU is already bottlenecking your 9600GT. If you upgrade the graphics card you wont see much of a difference due to being limited by your CPU. Upgrade your CPU first. You will need a CPU and motherboard upgrade as that motherboard doesnt support any recent CPU's. Probably ram also as new motherboards only support DDR3.
I agree with iam2the crowe, you should update your CPU, motherboard and RAM in order to not experience a bottleneck. Your best best would probably be an i3 2100 (some would go for a Phenom II [I have one and love it] but a recent Tom's article showed that the i3 was better in most circumstances even though it didn't have 4 cores) with 4GB (maybe 8GB since RAM is so cheap). After that, focus on a new graphics card. We need to know your budget. I know you said $200 for a graphics card (which is a good price point) but would you be willing to spend a bit more for new guts? Anyway a 6850 or better will definitely bottleneck your system (a 560Ti would be equivalent to a 6950). If you want to keep your current motherboard, CPU and RAM then I would suggest a 6770.