He doesn't need a cooler unless he buys a Skylake K processor, which he hasn't mentioned. All other Intel's include a cooler and certainly should be fine for a first build UNLESS he is going to overclock--in which case he must buy a K processor.
Dimerz:
For the same money as an i7, you might be able to get a strong i5 AND an SSD.
If money were no object, of course get an i7---but you are on a budget and from all I hear, an i7 adds very little to gaming. It helps when you can use hyperthreading--particularly in video rendering. Otherwise, you may not notice the advantage nearly as much as you would an SSD. The SSD has no major advantage in gaming either, but it helps a bit on many tasks and a lot on some.
If you insist on an i7, the 4790K or 4790 is probably a good bet. It has a very high stock clock speed. It's being replaced by the 6700 and 6700K, so it's starting to show up at a sale price. The main issue with it is the socket 1150 motherboard it requires---you'll likely never be able to upgrade to a stronger processor on that motherboard--the socket is about at the end of it's life. But it's very very strong otherwise. The 6700 and 6700K offer very little advantage----if you need an i7 at all. I'd get an i5 if I were in your shoes.
