Op, you will do fine with the fx 6300. That's what I have in my own system. When you can afford it, save up and get an aftermarket cooler like the cooler master hyper 212 evo(runs about 30 dollars in US currency). With that and having good airflow in your case you should be able to overclock. I clocked mine up to 4.3ghz which helps. If your cooling is good enough and depending on the board you can get, you may be able to get higher clock speeds.
I don't play far cry, but I've been playing wwe 2k15, civilization 5, assassin's creed unity on high (think I turned aa off but still pretty decent settings at 1080p.,other games, but those are newer ones I got that I can think of. Keep in mind the card I'm using is a Radeon 7950, so that way you kind of can compare.
For a budget board, I suggest the gigabyte 970-ud3p if it's available at a reasonable price. It's a little more than the basic boards, but should have 8+2 power phasing which is good if you want to overclock.