You should also understand that things are very different when it comes to CPU performance compared to 10 years ago. Back then, clock speed was an enormous factor. You could get a general idea of how powerful any processor was just by looking at the speed, and later, by how many cores it had. Then we hit a sort of power roof. CPU's were drawing too much power, so you couldn't just keep clocking them higher. That's when architecture became the focus, especially on the Intel Core series. Now you can't tell how powerful a CPU is until you look at all the specs.
You should also keep in mind that emulators vary on what they need. Dolphin, as I understand, relies a lot less on your GPU than on your CPU. I was able to run The Last Story (a little slowly) on an old Pentium with integrated graphics. My i5, however, can't run R&C2 on PCSX2 without some serious heavy graphic hacks, which make most textures look like a bunch of garbled pixels. The Wii is a good deal more powerful than the PS2, and yet Wii games way better than PS2 on integrated graphics.
If you end up going with a desktop and don't want to spend much money on a graphics card, I'd recommend the GTX 750 Ti. While definitely not the best card out there, it's amazing relative to its price. Maximum PC was able to get smooth 1080p on modern games when they stuck it in a $400 machine from Best Buy.