Here are the options I would choose from
eVGA 128-A8-N350 Geforce 6600GT $141
eVGA 128-A8-N343-AX Geforce 6800 128MB $189
XFX PVT40AUDF3 Geforce 6800GT 256MB $284
The Geforce 6800GT is by far the best but it the only one that slightly over your budget. If you can manage the cash go for it.
The Geforce 6800 is a little better then the 6600 for only a slight increase in cost.
The geforce 6600GT is the cheapest you want to go and still get decent performance
Now let look at how theses cards compare
Looking at the 3 graphs you see the 6800 get a average of 10FPS more then the 6600GT.
Looking at the 3 graphs the 6800GT gets a average of 16fps more then the 6800 and 27fps more then the 6600GT.