At that resolution you will be seeing pretty good frame rates even on a older Radeon 5770. so no doubt the 6850-6870 is good
Below is a chart. Straight from TomHardware benchmarks itself showing the difference in FPS at 1650x1050
Since you play Shooters i chose this one. Bfbc2 gets very respectable framerates with highest settings Including 8xMSAA and 16x AF
Now the radeon 6870 gets 8 fps on average more than the 6850
I wouldpay the extra 23$ for the extra performance. The more Fps the better
AS for your cpu the quad core will if you have the money be a better choice and be much more future proof then the dual core.
They both would last. But 2-3 years from now im sure many games would be utilizing more then just 2 cores. and with 4 cores you won't need to worry about your bottleneck as much. Also the intel i-5 has 6mb l3 cache while the i3 has 3mb l3 cache. So double the cache and cores = Greater speed, power, fps
And the one you looked at was the Intel i-5 2300 2.8ghz
ADD just 5 more dollars and get the
Intel i-5 2400 which is 3.1ghz stock .3ghz faster for 5 dollars. not to bad and you don't need overclocking.