i5 4670 bottleneck?

Hi, I'm building my first computer and trying to figure out which CPU to get. My graphics is a GTX 770. Will an I5-4670 non overclocked not be good enough? If overclocking is easy I could get the "k" model. The problem does my motherboard support it. I have the GIGABYTE GA-Z87X-UD4H ATX Intel Motherboard. Can I even overclock with this board? This computer will be used for gaming only which is why maybe I should get an i5.. and not an i7. I plan to get a good water cooler either way. I will be using a single 1080p screen. Does hyperthreading make a big difference? Is that all ill lose not getting an i7?

You already have a thread in general hardware, please post your question there. It's extremely confusing when you have a ton of different threads all over the forums as all the advice gets fragmented. It's pretty much the same people seeing your post anyway.