Mini-ITX Gaming & HTPC $800-1200

As your build stands, its relatively weak from a gaming perspective, for a $1000+ system. If a GTX750Ti is sufficient for your needs, then that's fine, but it does mean you are spending a lot of money on things that won't really make a difference.

CPU - You basically have to make the call for overclocking or non-overclocking, as they have a knock-on effect on the rest of your build. If you are going with a graphics card like a GTX750Ti then overclocking will make very little difference to performance, as you'll be graphics-bound in most games. Even with a high end graphics card, overclocking is very application dependant, and it's highly debatable as to whether or not it's worth the cost.
If you decide you want to keep that option, there's only one option, the 4670K
If you decide you want to streamline things, then go as cheap as possible really. The 4430/4440/4570 are all options, as at stock speeds all Haswell i5s are going to be very similar.

Motherboard - You have a couple of concerns here. Firstly if you pick the K-series processor then you need a Z87. If you don't, then you don't. If you need Wifi you can pick up a Wifi enabled board for under $100, and without for around $60. Secondly, cooler compatibility. ITX boards aren't standardised, so there are actually very few ITX boards a Hyper 212 will fit on. If you aren't overclocking, you can skip the cooler altogether, or go for a smaller tower cooler which will fit (think Hyper TX3, Hyper 101). If you are, then the 212 is a decent pick. It will fit on the Asrock Z87, but it will mean it'll be kinda offset within the Prodigy - not a massive issue but something to keep in mind. If you want it to sit in-line with the exhaust fan (which would be considered more optimal) then you need to get either of the Asus Z87 ITX boards, neither of which are cheap, but both of which have a central CPU socket.
Hope that's not as confusing as it sounds lol.

Memory - If its just for basic stuff+gaming, it's hard to see why you need 16Gb of memory. 8Gb is loads for modern games, and the only time I've managed to exceed this was running multiple game clients and near to hundreds of browser tabs. It's a good place to save you some money.

PSU - It's not ideal really. The Prodigy does have space in which you can kinda tuck+fold cables, but with a 750W non-modular PSU there's going to be a lot of spare cables, especially if you use a GTX750Ti. It's worth also mentioning that the setup as listed is a couple of hundred watts at most, so given your budget you'd probably be better off grabbing a quality entry level PSU in the 400-450W range. Hell, a 500-550W PSU will power basically any ITX build, and you can get a great one of those for ~$50.

Graphics card - This is totally up to you. In any gaming build, the graphics card is always likely to be the most expensive part, as it's the big performance dictator, and in a $1000+ gaming build, you'd definitely expect to see something more in the $250+ range. It's certainly doable within your budget, just by shuffling funds around you can get anything up to a GTX780 I think. That might be overkill of course, but there's likely to be a happy medium in there somewhere, depending on the types of games you want to play.