AMD gives more cores for the same price, but Intel CPUs are more powerful per core. I am not sure how useful having more than 4 cores even is. Also, I think AMD is not putting the effort into CPU development that Intel is, but I can't really cite any facts to back that up. I just think that AMD is more interested in competing with Nvidia for the GPU market right now. I think a Skylake CPU will serve you better down the road, than anything AMD has to offer.
Skylake is made for overclocking, so I included a liquid cooling system, even though my own PC just uses air cooling (I can't over-clock my CPU). The motherboard was a compromise between price and features, this one seemed to have the features needed to take advantage of new tech, without being too pricey.
The RAM I picked is supported by that motherboard - when it comes time to buy make sure the specific RAM part # you purchase is supported by the motherboard you purchase (consult the manufacturer's website for that board). Skylake processors can handle RAM frequencys up to 3600 MHZ, but RAM that fast is much more expensive than 2800 and 3000 MHZ, and I am not sure which Motherboards support those RAMs.
The SSD is M2 interface, which is supposed to be noticeably faster than a SATA connected SSD. I have a SATA connected 840 Evo (previous version of that drive), and it is very quick. Your OS should go on the SSD, and your boot time should be quick and general OS functioning should be snappy. The Toshiba HDD is just for bulk storage, and maybe for games. I put games on my HDD, instead of my SSD, and they seem to run fine. They just take longer to start up initially than if they are on SSD.
The choice of GPU's was fairly arbitrary- I added everything else to the build, and then picked a GPU that was high-end but would bring the total to close to what you stated your budget was. I did little research on GPU's before selecting it, you might want to research that more closely or solicit opinions from the forum here.
I chose the Antec power supply for 2 reasons: it was low cost while providing enough power to cover you even if you need to add another GPU down the road (and who knows what else); and Antec is a decent brand, and I think there PSU's have a decent rep - even though SeaSonic and the higher end Corsair PSU's have a better rep (they are also more expensive).
The choice of case was also fairly arbitrary, I thought that surely a liquid cooling system made by Cooler Master should fit easily into a case made by Cooler Master. I selected one that had high reviews at PCPartpicker. I also picked one that was a mid-tower ATX case, with front-side USB ports.
I should also add that just a few days ago, I got curious about what a Skylake based system would cost and what hardware I should put into one. I did a dummy build at PCPartpicker and bookmarked it. The build I put into post #2 is essentially that build, with some stuff omitted (monitor, keyboard, mouse, DVD drive, speakers).