yea you aint need overkill PC, considering you also need monitor ETC,for editing videos at that pricepoint (considering monitor ~150-200$) you should lean towards AMD CPU,some moderate gaming card and generally basic set so eh here it goes:
AMD FX-8320E Octo-core, intexpensive as for 8-core,only 95W TDP excellent for multitasking,decent for gaming also
Radeon R9 270X (or R9 270) it may have issues handling the very latest games on ultra, but for games like ones you mentioned, max settings no problem.
WD 1TB 7200RPM HDD
some moderate AM3+ board, my recommendation is GA-970A-UD3P , it is fairly enough to allow your CPU overclock well
8GB RAM, speed (1600,1866,2133 etc) and 2 or 1 stick is really a preference thing, though picking faster RAM and 2 sticks instead of 1 might give you a couple extra FPS.
Aftermarket cooler-go for something basic like coolermaster hyper TX3 EVO or hyper T4
A metal box,a.k.a case to put em together.