Before we go any further, I feel the need to point something out. There are a lot of processors out there, and the market is rapidly changing, so it's impossible for me to tell you the exact processor you need. All I can do is offer pointers and guidance based on your needs.
Let's break down the market into four segments:
This territory is a fight between AMD's Ryzen 3 and Intel's Core i3 chips.
Right now my recommendation goes to AMD and the Ryzen 3 chips for the budget segment. You can pick up a Ryzen 3 1200 for $110. For that price you get quad-core/four threads, an unlocked multiplier for overclocking, and a fantastic cooler.
And if you don't feel the Ryzen 3 1200 offers enough power, then for an extra $20 you can have the Ryzen 3 1300X which has a faster clock speed and boost.
And on top of that all AMD Ryzen chips are VR-ready, which gives you some future proofing.
If you are on an ultra-low budget, then an Intel chip such as the Pentium G4400 or G4560 (which retail for around $55 and $79 respectively) are worth considering.
At this price point we're looking at AMD's Ryzen 5 squaring up against Intel's Core i5 silicon.
While the mainstream is currently dominated by Intel Core i5 chips, many of Intel's offerings in this bracket don't have hyperthreading, which means you get one thread per core, as opposed to AMD's Ryzen offering which all offer two threads per core (if you're confused by threads, just think "more threads = better").
This means that a chip such as the quad-core/eight-threads Ryzen 1500X priced at $189 is a better choice than the similarly priced Intel Core i5-6400 which doesn't have hyperthreading.
At the higher-end of the mainstream market, again, AMD's six-core/12-thread Ryzen 5 1600X stands head and shoulders above anything that Intel has to offer in the same price range, although at $249 (cheaper if you shop around) it's at the very high end of mainstream.
This battleground is between AMD's Ryzen 7 and Intel's Core i7 silicon.
From a performance-per-dollar perspective, the Ryzen 7 silicon wins hands-down, with the top-end 8-core/16-threads AMD Ryzen 7 1800X retailing for only $499, compared to the 8-core/16-threads Intel Core i7-7820X, which retails for $599.
The smart money buys AMD silicon.
But if performance is the ultimate deciding factor then you're better off going for the i7-7820X. The differences aren't enormous, and vary depending on what benchmarking tool, game, or applications you're using, but the raw power advantage goes to Intel here. But you're paying dearly for that slight advantage.
We're now at the point where the question isn't "how fast do you want your PC to be?" but "how fast do you want to spend money?"
Here the battle lines are drawn between AMD's Ryzen Threadripper and Intel's Core i9. Specifically, the Ryzen Threadripper 1950X and Intel's Core i9-7900X (although there's an upcoming Core i9-7920X that's been making cameo appearances in benchmarks).
Either path you take, you're looking at a lot of money here. The 16-core/32-thread Ryzen Threadripper 1950X costs $1,000, with the 10-core/20-thread Core i9-7900X costing $1,030.
Which one is best? Well, it's hard to tell. While benchmarking and testing seems to suggest that the Core i9-7900X wins in terms of raw horsepower, the Ryzen Threadripper 1950X has faster multi-core and overclocking performance.
If I were spending +$1,000 of my hard-earned cash on a processor, my money would be buying a Ryzen Threadripper 1950X because of the faster multi-core performance, and because it seems to offer more in the way of overclocking.
That said, at this sort of price point, whichever processor you chose, the bottleneck is not going to be the CPU.