With Skylake there has been a few good cases to made with going with a 6700k over the 6600k for gaming. It can improve FPS depending on the program in questions. Beyond those few cases, most games will likely be just fine with the single threaded performance of an i5 and the difference in price would be better put to cooling and or a newer GPU. However if you are going to be using a lot of programs that can take advantage of multi threading, then a i7-6700k would likely give you more overall performance gain, and the i7-6800k a further boost with the extra two cores. Really it comes down to the core purpose of the computer.
As for cooling, if you're going with air cooling, the Cryorig lineup has some good coolers for not a hell of a lot. The H7 and H5 Universal have no RAM overhang and the H5 Ultimate is a good lower price alternative to the D14/D15 from Noctua. Even if you end up not going with any real serious overclocks, the H7 makes for a very good low noise cooler that comes in with better performance and lower profile than the Cooler Master Hyper Evo