I would vote for a I5-7600K based gaming build.
Primarily because games depend most on single thread performance, and the Intel chips have better performance per clock.
Add to that, a I5-7600K can usually be overclocked near 5.0.
As of 1/13/17
What percent of samples can get an overclock
at a vcore around 1.4v.
I5-7600K
5.1 28%
5.0 52%
4.9 72%
Ryzen will top out about 4.0
Then, few games can make effective use of more than 2-3 threads.
If you play such a game, the I7-7700K will be $100 more and arguably the strongest gaming cpu available today.
On the two builds, there are other trade=offs available.
1. I would always include a ssd for windows in any build today. Samsung EVO at 240gb or greater is the best.
2. I have no problem busting a budget for a great case. It will be with you for a long time.
But, $300 for a Corsair obsidian seems a bit much.
Functionally, you can buy a good case for 1/3 as much.
So long as it fits your motherboard and has two 120mm front intake fans or better, you will get good performance.
3. Likely you do not NEED an optical drive.
Windows 10 comes on a usb stick.
Still, A dvd burner is cheap so I would include one if your case has a space for one.
You may find it convenient to initially load the motherboard drivers and software that will come with your motherboard.
Lastly, two tips:
1. Buy a #2 magnetic tip Philips screwdriver for assembly.
2. Download and read, cover to cover your case and motherboard manuals while you are waiting for delivery.