For AMD I would not suggest anything less than a 8 core FX. For Intel I would go with a i7 or fast i5. I don't like using the PLX chip so if you can swing it a 5820K or something with more than 16 PCI-E lanes is nice.
But there right the AMD FM2+ CPU's even fast ones like the 860K don't scale well. Even in two way crossfire scaling is worse than a FX 4 core or Intel. In 3 way its a lot worse.
You can see in this article how a FM2 processor does. The AMD A-10 5800K: http://www.anandtech.com/show/7189/choosing-a-gaming-cpu-september-2013/6
Threeway anything just isnt worth the work (or the special equipment your gonna need to even run it). Two- way, sli or crossfire is fraught with issues. I would consider a much stronger single gpu. I normally run multi gpus not for the crossfire per say but more for pushing multiple monitors. Both sides are pretty hit an miss about the positives about multi gpus configs.
7950s aren't too demanding an i5 or even something like a FX-6300 overclocked would be able to keep them fed, if it were my money I would get either 4690k or a FX-8350 or better if you can afford the motherboards with better power delivery. The i5 will overclock decently and is very powerful, the FXs will overclock lots and will suffice. i7s are great for this kind of build but they are expensive and given that you are using older GPUs seems a bit overkill.
The other thing I would say is make sure to do your research on the motherboard, 3 way crossfire isn't that uncommon but make sure it has good support for it. 8x 8x 4x would be on the edge of barely acceptable but, more PCI-E lanes is better and would be more usable in the future. this being said a question: does it not make more sense to use a more powerful GPU like a 970, 780 or 290x the later two have come down lots in price, and a cheaper CPU and MB netting you less power usage, lower overall temps, and a better game-play experience?
An old Ivy Bridge i5 with a z77 motherboard would have all the juice you need, and the motherboard would be able to handle the crossfire. I think the motherboard here is jsut as important as the CPU. An FX-8350 might be a fine CPU, but what 990fx motherboard could take the three cards effectively? I think the most cost effective would be ivy bridge. You could go Haswell i5 and get a z97 or older z87. I would just look for good motherboards and purchase based upon price. There is absolutely no reason to spend the money on x79 or x99. thatis just crazy, unless you are doing something more than gaming.
I always suggest microcenter or Fry's. I sent a friend to microcenter to get my processor last week. A i5 4590 for 150$. If you don't mind going back a gen. When I was in Fry's in Seattle they had a i7 3770K for 210$