3570 and 3570k are basically the same except for the unlocked multiplier. I currently run a 3570k and have OC it from stock 3.4GHz, to 4.2GHz with nothing more than shifting the multiplier in Bios. Took 3 seconds.. and I can see the difference. If however you are not going to overclock, for whatever reason, save yourself some cash and go with a 3350P and a B75 or H77 mobo, the 3350P being best 'bang for buck' chip, and you won't need a Z rated, overclocking board for a locked chip.
The 7870 will work ok, in the heavy games like BF4 now, but I wouldn't expect to see too much out of it there. look for medium to high @1080p and @30-40 fps