A lot of the differences in the CPUs of AMD vs Intel really come down to a few things, mostly involving the actually architecture design and the build of the processor.
With Intel, you're going to get a more expensive CPU, but it has a better performance per dollar. Comparing single core performance...Intel will win 9 times out of 10. They do a lot of things better than AMD, which of course means the price will go up. But generally speaking...the mid-range i5 CPUs should be able to outperform any high-range AMD CPUs. Oh, that's another thing...if you're going Intel...pick an i5. i7 processors are really only meant for PCs that will be doing media work all day (video processing/graphic design/audio/etc). If you're just doing gaming/web browsing/normal stuff...and i7 is overkill.
That being said, AMD does some things better. They are better for overclocking (also more frequently found than Intel CPUs), and generally the on-board graphics options on an AMD processor is better. And they are the budget choice. On the lower end of things, they will be the better choice.
Conventional wisdom will say: If you're on a budget, go AMD; if you have the money to spend, go Intel.
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Investing in a GPU vs a CPU entirely depends on what kind of gaming you're going to be doing. I'd just suggest a GPU, as it will make your life easier if you want to play more than Rocket League/WoW/LoL. Now, what GPU you get is a different animal...
The conventional wisdom above becomes more tricky when you're in the market for GPUs, as the AMD vs NVIDIA war is monstrous and always changing tides.
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I highly urge building your PC. It's not difficult, and the mixed warranties are a non-issue, assuming you don't blow your PC up. For the price of a pre-built, you can build a better PC, because pre-builts are going to be marked up. Building one will also help you learn more about how your computer actually works, which is handy.
It also gives you something to be proud of
There are a toooooonnnnnnnnnnn of YouTube tutorials and whatnot to help you, and the internet has plenty of resources for troubleshooting/maintenance/etc.
Now, to add onto the building PC thing: Deciding between AMD and Intel is very important, since it basically determines your entire PC. CPUs come in varying sockets, with AMD/Intel being entirely different. Motherboards only take certain socket types, so you really need to double-check compatibility.
I'm totally willing to share my experience and whatnot with you, though I would hazard to say most of what I say could be found online.