Get fx6300,apt for the workloads here,quite a good processor for the price and also quite fine for gaming.
As far as crysis 3 is concerned different sites have different results,as they have mostly tested on different parts.
Techspot's results would conclude fx4300 being better than i3 3220 but a tomshardware test results would show the things other way around.
In metro:last light test results from techspot,i3 3220 was a somewhat ahead of fx4320.
As of now between the fx4300 and i3 3220,they perform close with i3 3220 winning in more occasions,though generally close at 1080p.The HT does help it out in quite a number of games.In Metro:last light fx6350 which has near about same clocks as fx4320 but higher core counts was significantly ahead of the latter in the tests.
For monitor you can look for Dell S2240L ~8.5k.BenQ RL2240H is a TN panel based monitor.
S2240L would have better viewing angles and color production.