What cooler to take for this build??

Yes, any compatible one, the more expensive the better... and that case fits and does not interfere with memory.... And so, all that for 1K rubles fine cool. And so, still depends on whether the Prots to chase, and how. They are cool now, too much bother if there is no acceleration, it makes no sense. If Yes, more expensive cooler, if not, you don't need to. The same Zalman or thermaltake or Cooler Master will fit.

And yet, look at the substrate, the direct cooling of tubes, but it should adjoin densely to the processor. There are coolers, even expensive, but there are 4 thermotrace, and in between the gaps... it Is not desirable.

any lga 1151 socket

http://www.dns-shop.ru/product/e22fb60689b0526f/kuler-dla-processora-deepcool-gammaxx-300/

quiet and efficient, perfect for the money.

By the way, here in the cooler in the above comment, you may notice that token, I'm talking about. It is seen that copper tube going from the aluminum base, and in the photo, where the base is large, it is seen that the thermal interface is a little bit not exactly lies. tube above, the rest below, and the gap is small... overall not terrible, if a good thermal interface, but it is better when monolithic medaka, or at least all is well sanded.