If you're just starting out, you could look at simulating your robot first, as you will hit a lot of the same issues but will be a lot cheaper. Gazebo will allow the solving of a lot of higher level issues and will help you discover:
1. problems with your design,
2. the software configuation you need to support your robot's tasks
Once you know the software configuration, you can start looking at cpu's. My preferences is for the beaglebone, an opensource Armhf device, running ubuntu. I believe its perfect for mobile devices, however because it is different architecture to an x86 machine, pretty much all your ros source code will need to be compiled on the bone as support for cross compiling is a little deficient
Hope this gets you started. And if you need an ROS ubuntu SD card image for beaglebone, let me know, as compiling from source can be a little tricky.