We now have benchmark results for the new Ryzen processors from AMD and overall they look very good. There are some issues with 1080p gaming where Ryzen only performs at Haswell level, however in workstation loads Ryzen is a beast even outperforming the i7 6900K with costs twice as much. Gaming in 1440p Ryzen trades blows with Intel's best, coming very near equal to the i7 6900K. So you are going to have to decide if gaming in 1080p or gaming in 1440p / 4K is more important to you, because based upon that information the recommendation is going to be vastly different.
If you are interested mainly in 1080p gaming then you best bet is either an i5 or i7 processor, and a GTX 1060 or 1070 would be enough to max out just about anything in 1080p. Between the two processors the i7 is much more "future proofed" as there are already a lot of posts explaining that right now and going forward the i5 is no longer the "king" of gaming. Many modern games coming out are optimized for multiple cores and can even use 8+ in some cases, and there are a few that can even make full use of the i7 6900K as it bests the i7 7700K in a few titles due to extra cores and threads. Gaming going forward is going to see the i7 7700K reign as the new "go to king" of gaming, that's not to say an i5 still won't run the game but it will no longer be equal to an i7 in gaming. In modern games the i7s are going to distance themselves from the lower core / thread count i5s.
If you are interested mainly in 1440p / 4K gaming, then that is a different beast all together and the recommendation shifts to AMD. In testing at 1440p / 4K the new Ryzen processors keep up with Intel's best in most titles, coming within a few FPS. There are much better priced AMD options than Intel options in this field and in fact its cheaper to by an 8 core 16 thread Ryzen R7 1700 than it is to buy an 4 core 8 thread i7 7700K, and at 4K with a GTX 1080 the performance difference is very slim. As a bonus if you do anything else you have an additional 4 cores of processing power with the R7 1700 making them more "future prof". The very best option though may not have even hit the market yet. AMD is set to release Ryzen i5 6 core 12 thread processors next month and for pure 1440p / 4K gaming (with either a GTX 1080, GTX 1080TI, or AMD Vega GPU) it may prove to be the best "bang for your buck" 4K gaming processor available.
For pure 4K gaming I don't recommend an i5 as at 4K they are not keeping pace with i7s or the new AMD Ryzen processors. i5s are great at 1080p but struggle at 4K when benchmarked next to i7s or the new Ryzen. i7s are very good at 4K gaming, however you will also pay a premium for them. 4K gaming is where Ryzen comes very close to the best Intel has to offer and at a much better price point.