I would get Intel Skylake CPU, cheaper options than 6600K will be available soon. Here is a build for $715.95 after rebates with one:
Link
Can be cheaper if you get better offers on a GTX 970 like already posted on this thread. Also with cheaper CPUs available soon and cheaper Skylake motherboards, should get closer to $600 for the hardware.
Save yourself $65 and go with the GPU I listed above. Maybe consider a slightly higher end mobo (make sure you have enough fan headers and sata ports). I would at least purchase one that has been reviewed online and by actual customers (search Amazon and PCPartPicker reviews).
As I said, most people will tell you to go with Intel. I still stand by my statement however. Since we are going by cheap, and by benchmark. An FX series processor will give you more bang for the buck. I had a lower end i5 processor that cost more than what I paid for my high end FX processor. Benchmark test will vouch for it. A high end intel will of course out perform an AMD in almost all aspects (graphics is actually the one place AMD beats out Intel) but, you will pay nearly 500, probably more, as opposed to 200. On average, intel mobo's are more expensive as well. As far as GPU, I'll need citations, my experience and those I've read usually put the Radeon and the GTX series GPUs at pretty even in terms of quality and power. Water cooling provides a cheap cooling solution that works far better, is affordable (start kits begin at $50 +-) and is far quieter than a bunch of fans. It was more of a suggestions. And yes, you probably could run 650w, but I have a feeling that you will be over the 75% threshold. PSU's peak at their stated wattage, much like a car amp. However, it generally can't sustain that amount for any serious amount of time. 600w give or take is more likely the max, depending on quality of the PSU (I believe 90% of labeled wattage is considered high quality, 80 and above average and below poor). Much like storage, memory and cpu, when you are humming a long on an average day, you dont want to be holding your PSU above 75% capacity. I am guessing with a 650w PSU, you will be close to that. 850w insures that not only are you not tipping over 75%, but you won't top out in instances where you might peak out the system.
First, I greatly appreciate the detailed and civil response. Pretty rare these days.
I can't argue against the fact that AMD CPUs are cheaper and assuming you are getting a GTX 960 or Radeon 280 level GPU, won't really hold you back. At that point, I agree 100%. Anything above that and, there just isn't any point to an AMD CPU. Not to mention
AMD CPUs are more power hungry and produce more heat as a result (even worse when overclocking).
Benchmarks have no relation to gaming performance, which greatly favors Intel. This also factors into future upgrades. Lets say in the future you get some more money and want to upgrade to a better GPU, 980, 390X, or maybe even a Fury or 980ti. Guess what, you AMD CPU is going to be a bottleneck. Then you will have to replace your CPU and mobo... not a very enjoyable task... also not cost efficient.
Those prices differences are an exaggeration. There are plenty good ~$100 Intel mobos and a 4670/90K can be had for around $225. So I have no idea where you are getting $500 from. We are not talking about 5930k vs FX-8350...
Nothing against AMD GPUs, they have terrific cost to performance ratios. Although, they are
definitively more power hungry and run hotter (second link). This has a ripple effect of requiring more cooling and PSU wattage and thus extra costs to lower temps/noise. Still, great bang for the buck.
A Cooler Master Hyper 212 Evo is $25 and will quietly cool any i5. Unless you heavily overclock or have a power hungry CPU (ahem... AMD... also i7), watercooling is not necessary. Again, this goes back to the cost of an AMD processor. You may save $50 on the CPU and maybe $25 on the mobo, but that savings will be cut by 30-50% by needing and AIO cooler. AIO coolers are also not guaranteed to be quieter. A bad AIO can be worse than a good air cooler. Again, case layout > cooling solution.
In therms of PSUs... when gaming you are not taxing your PSU at 100% the entire time. First, your CPU is never going to run at its max TDP when gaming. Your GPU will more than likely vary but won't be stuck at 100% draw, 100% of the time. Again, one of the advantages of running Intel/Nvidia is that both components are far more power efficient than AMD's comparative (performance) offerings.
A 4690k/GTX 970 could get by with a 550W PSU and never break a sweat. Unless you have like 5 storage drives, 4 fans and overclock everything... you won't get near 90% of 650W. 850W is way way way overkill.
I have an i7 4790K and an EVGA 980 TI Classified with an EVGA 850W Gold PSU in my system (note estimated wattage and multiple by 1.2-1.3). The 4790K is at 5Ghz@1.37V and the 980 ti is at 1500/8000Mhz at 1.23V (both measured with a DMM). My PSU fan isn't audible when I play GTA V in 4K (audible range is ~>70% load).
There is no question, in the $500-750 range AMD CPU and GPUs are viable options. However, in my opinion (see above), anything higher than that and it is better to go with an Intel i5 CPU and Nvidia or AMD GPU.