The mot powerful companion computer hardware solution at the moment is without a doubt the Jetson TX2. But the easiest to develop for is probably the Intel Edison, since you can prototype actual run-time algorithms on a normal desktop computer. Just don't expect it to run the latest in computer learning, or any kind of high speed, high resolution dense (motion data for every pixel) optical flow computations etc.
How to connect Jetson TX2 to Pixhawk 2.1 and camera
Just grab navio2, raspberry pi, raspi cam and 4g!
I would go with Pixhawk 2.1 with Edison carrier board, Here GPS and the Edison. If you want a second computer, I would suggest the Odriod XU4 or if you have the budget and room, NVidia TX1. If you need help building your drone let me know.