I'm guessing OP is encoding for the AppleTV so target is probably MP4 and not MKV.
I agree with the suggestion for a quad-core Sandy Ivy Bridge (gah, still on a 2011 mindset). If you want to save money, a Core i5 would be fine. HyperThreading on the i7 makes for 20~30% speed up in x264 over a similarly clocked i5. Whether it's worth the extra $100 or not is up to you. Imho, since you're likely spending quite a bit on the entire PC (probably around $1000+ if you're planning on cramming it with HDDs), might as well go for the i7 for the minimal price increase.
While augerpro didn't find QuickSync quality acceptable, I think it might be worth testing yourself. While all QuickSync capable encoders I know of are paid, most offer a free trial and the time savings can be quite significant.