Here you go. The FX-8350 (with 8 cores) is overkill for gaming because 4 cores is the max for many games and a lot of games are still utilizing only 2 cores however, you will see the performance in applications that can utilize all 8 cores. I would have went with Intel here but you said you wanted to oveclock and the overclocking Intel CPUs are out of your budget range. The 7850 is a good card and can be overclocked to meet 7870 specs. You definitely need an aftermarket cooler if you plan to overclock.
Fitting a monitor into a build for 700 dollars with a 6300fx is difficult. I'm not sure where I'd cut corners on the parts, and it would only be 10 or 15 dollars for a few parts. This is what I came up with though: