As long as you get an x86 or x86_64 processor, you will be fine. Almost all of the computers sold today come with one of those. AMD or Intel doesn't matter as much as GPU selection.
Also, if you don't want to deal with Windows 8, you can always build your own computer. I'd say if you're smart enough to install Linux with the manual partitioner, and you can replace or install any computer internals, then you shouldn't have a problem building your own system.
Used systems are another option. Another member of this forum got a server-class system for under $500.
Running on a 4-slot toaster @ 60Hz