CPU
Very good overclockable CPU. It fits well into the budget, but for gaming you usually won't need more than an i5. Technically they are both quad core but i7s have hyper-threading, meaning they essentially duplicate the cores making it more like an octo-core. The i5-6600k will be more than fine if you want to save $100.
CPU Cooler*
Very solid CPU cooler, you will be able to do some light overclocking if you want, but you likely won't need to for a few years at least.
Motherboard
One of the best motherboards on the market. Probably a bit overkill but given your budget it is probably worth it. Very high build quality and allows for easy overclocking and upgradability in the future.
Memeroy (RAM
8gb is standard and this is very fast RAM. Pretty standard not much else to say. You can always go for 2x8gb and get 16gb but that isn't really necessary, up to you.
Storage
SSD is very fast, you can install OS and some of your favorite games on it. Added a 2tb HDD because it is hardly more expensive than many 1tb ones and you can use it as mass storage. Well reviewed, not much else to say.
Video Card (GPU)
Honestly if you can wait a bit I would go for RX 480 which is releasing soon and will be probably a bit better than the 970 for $200-$230. It releases June 29th. However, if you're willing to pay a bit more 1070 is also very good. It just released and will be able to max any game at 1080p 60fps. 970 is still good just in an awkward spot because of the new cards releasing.
Case
This is a full tower, meaning it is quite big. It has great aesthetics, and plenty of room. You can add some nice fans for some cool looking lighting for relatively low cost. I actually just bought this case and love it. Not much else to say, just a really solid case.
Power Supply (PSU)
Very high quality and well reviewed. 750W may be a bit much but it allows for SLI or crossfire in the future as well as overclocking.
Optical Drive
Allows you to watch DVDs, listen to CDs, but most importantly install OS off the disk. Not much else to say.
Operating System (OS)
Very standard nothing really to say.
Monitor
Well reviewed 24 inch 1080p monitor, the monitor is more preference based so you can feel free to change if you want.
Keyboard
I use this keyboard. It is great quality with LED lighting as well as plenty of keys to macro and software to program macros. Again this is basically personal preference.
Mouse
I use this mouse as well, very good mouse for a fair price. This is up to you mostly, this is just my personal preference. If you want Logitech you can get the G502 for around $80, I just didn't think it was worth the extra cost.
PCPartPicker part list / Price breakdown by merchant