I'd say you should take a look at the Raspberry PI for the time being. It cannot do it all alone, you will have to combine it with a real micro controller as io expansion.
- The raspi is cheap, and got a strong community, easy to get help when you are stuck.
- For micro controller I would chose an ATmega328 from Atmel (~$4 on ebay). with that one you can stay Arduino compatible, which again has a super strong community.
I know the newer BeagleBoneBlack will be able to handle both tasks in one unit, but the product seems to be a little less mature right now, and the community is nowhere close to raspi or arduino!
Over at LetsMakeRobots we are building robots too, some even as advanced as your project, you might find some inspiration. And there are definitely some motor driver geeks there!