That price I came up with is based on what I'd consider to be the best performing consumer grade hardware available.
The extreme series of CPUs are bad value for the $1k price considering that the best consumer grade processors
perform similarly at a fraction of the price. Most people wouldn't consider the extra few percent in some limited scenarios to be worth the extra cost.
Intel i7 5960X - $1050Intel i7 5930K - $580Intel i7 4790K - $340Intel i7 4790 - $310Intel i5 4690K - $240Intel i5 4690 - $225The "K" suffix means it has an unlocked multiplier, so good for overclocking. Otherwise, money can be saved by getting the same model without the suffix.
The added cost of the extreme series can mainly be attributed to the presence of more physical cores. The performance the individual cores across most of the higher end CPUs is extremely similar. The only advantage of the i7 series itself over the i5 series is hyperthreading, which offers little to no advantage in most situations. The i7 series is regularly cited as being better for people who almost exclusively use software that can actually take advantage of multiple cores, things such as video processing or 3D modelling. With a single application using many cores, there is the penalty of managing the concurrency which in turn slows things down. Even the OS managing different applications is going to encounter the same problem. In typical real world situations the difference between different models is smaller to non-existent.
The best bang for buck high performance CPUs are the high end i5s. Anything higher gets hit by diminishing returns in performance vs price very quickly. Even a low end i3 would probably outperform your old system with ease. As I said before, the Skylake 6k lineup is in the process of being introduced at the moment, so it might be worth waiting a little while for something better.
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GPUs are usually the biggest rip off in a build. A new lineup each year and the difference is usually more marginal than with CPUs, but people will happily tell you the complete opposite depending on where you ask. Then there are different models specifically for niche features like 10-bit colour, gsync/freesync, and so on.
I really don't know how you expect to test high resolutions. Most GPUs will refuse to output anything above what a monitor supports natively, and most monitors aren't going to attempt to display anything larger than what they can handle. Trying to output 4k onto a 1080 monitor isn't going to end well. I have all those problems and more with my own GPU, which often refuses to output display modes that my display does happen to support.
Most of the high end CPUs these days actually double as GPUs if you have a compatible motherboard. A good discrete GPU will typically perform better though. I hear it's driver support that keeps Intel GPUs down.
There isn't anything else in a system that would or should cost anything close to the CPU or GPU. Motherboard, RAM, and a PSU are much smaller expenses in comparison. At any rate, you should consider being a bit more economical, especially if you intend to buy with other people's money.