*For people like me that skim through articles before reading, I have bolded the most important facts.
I have a 7850 and an i7-2700k and I am able to play PS2 games, WII games, Dolphin games, DS games, all Mame games that I have tried, and every older gen console. Nowadays, Emulation for everything up to a PS2 and Wii can be achieved for around 400 dollars. If you want to use filtering in the games at 1080p resolution, than a 600-700 dollar computer would suffice. A big problem with Emulation is not entirely hardware, but also the software used. Make sure you do research and find which Emulators emulate the best.
This is a link to a pretty accurate table where CPUs are listed out and are given a tier based on how well their performance is with Dolphin. Keep in mind that Emulators will mainly only use one core.Some Emulators support two cores, but not many do. This means that a 6-core AMD cpu may not emulate games as well as an Intel two-core cpu because single-threads are better with Intel. For your case in particular, because you want to use your pc for emulation, than an Intel i5-3570k or an i7 may better suit your needs. In fact, an i3 would have better performance in emulation than the Fx-8350.
When talking about the GPU, Emulators will not use GPUs unless filtering and a high resolution is turned on. Some emulators may still use the GPU, but the GPU is NOT as important as the CPU. For example, a Pentium G860(Dual Core Intel CPU) with a 6670(AMD Low-End GPU) will play emulated games better than an A4(AMD dual core CPU) with a 7770(AMD Mid-range GPU).
Ram generally doesn't effect Emulators, but will effect it if you have too little ram(1GB) and are running other tasks in the background.
Just to reiterate, A Cpu is the most important thing. Make sure when buying a cpu, Single-thread speeds are fast. A GPU will handle the graphical aspects of Emulation. If you want to run 1080p with many filters, than a high- mid end GPU will be needed. If you want to run games at native resolutions with graphical settings at the lowest, a low end GPU should work.
Also, I am not an Intel fanboy. I have been through many computers and have tested many of them. What I say may and or may not be the truth, but I'm glad I'm able to share my knowledge with you all.