EDIT: Might as well just post the whole system that I built:
http://pcpartpicker.com/p/BYnmBm
I love it, silent, uses 40ish watts to run MC at 100 fps, cold boots in 10 seconds (OS = Lubuntu 14.04 LTS), and only cost me $440 shipped. Part Picker throws a warning about the video card being too long and it is
very very tight and I had to build things in an odd order, but it did fit without any grinding or cutting.
This is what I went with for a few reasons:
Intel Pentium G3220 Haswell Dual Core @ 3.0GHz LGA 1150
1) This computer is really only for playing modded Minecraft
2) Minecraft is not multithreaded so no point paying for extra cores which will sit idle
3) I didn't want to spend more than $500 on the whole computer
4) LGA 1150 is new enough that I can pair it with good but still cheap mobos
5) Uses very little power - it is hot here and I don't like paying for heat only to pay again to move it outside
I'm able to play DW20 1.7.10 v1.0.3 and I never encounter lag spikes of death which is basically all you can ask out of a proc. The video card is a 750Ti which does 200 fps no problem.