You should consider putting together a thread with details on the cheapest computer(s) to build that can run PM well enough for netplay.
Obviously sustained 60fps is a must, and assuming plenty of peeps will want to play a LOT (myself) being able to do it without overheating is a must.
I'm going to find myself wanting for that kind of info come this summer, when I won't be able to rely on my roommate's gaming laptop.
If you want to build a budget computer that will play on NetPlay, you should head over to the
Dolphin Hardware Subforum. They're very good at recommending budget setups. Just let them know you're on a budget and provide the games you'd like to play.
My recommendations on the budget intel side (which will have vastly higher single threaded performance [better in Dolphin] but inferior multithreaded performance [general computing]) are the Pentium G3220 and the i3 4130. The Pentium has a solid single threaded performance which will certainly play Project M at full speed. It's one of the best price per performance processors - I believe it is around $60. Don't let the Pentium label deter you it's using the newest Haswell architecture. For about $120 (still pretty cheap for a cpu), you can get the i3. The i3 is about 15% faster in dolphin and 30% faster in everything else.
On the AMD side I recommend the Athlon 760k. The Athlon will run Project M at full speed and costs around $80. It is about 20% slower in Dolphin than the Pentium and 45% slower than the i3. However it will be faster in multithreaded performance than the Pentium, yet still worse in multithreaded than the i3.
If you're really willing to dig deep the i5 4670k or the i7 4770k are the way to go. They will be much more future proof and will run most Dolphin games at full speed, as well as blow the previously listed processors out of the water for everything else. They cost $230 and $340 respectively. The i7 is generally considered one of the best processors to date.
tl;dr: Pentium G3220 will be the best for a budget cpu catering Project M. It will be a little slower for multithreaded things so if you plan on using other things get the Athlon 760k (it will be worse in Dolphin), or if you're willing to pay more, the i3 4130 (better in Dolphin). If you want a more future proofed cpu invest in the i5 4670k or the i7 4770k.
Also check out
PC Part Picker to pick out the parts for your rig. It's amazing because it makes sure all the parts are compatible, and finds the best deals online. For the rest of your build, just make sure you get a decent cpu cooler (you want a good one because Dolphin does a great job and generating heat, but you don't need liquid cooling or any of that ****), 4gb RAM (unless you want more for your other needs), a decent video card and keep in mind Dolphin requires almost no video card to run due to the fact that it's almost all cpu but if you want to play with 4x IR I recommend the GTX 750 or Radeon 7790, a PSU that has enough power usually need 400w+, and a hard drive that has enough space for all your Dolphin isos. Good luck building!
I've also included this post on my
Project M Dolphin Netplay Guide for others to see as well.