I would think you'd want more than 10 ahr in the battery, minimum. More if you can get it. But the system you want to build is kinda alien to me. I have only built this one ebike that I ride. I like Frank's idea of getting some of the guts out of one of those little elderly person scooters. Or maybe check specs and hardware for a few electric wheel chairs. I would think you could learn a lot by studying websites like this:
Electric Wheelchair SuperStore - Power Wheelchairs, Pride, Jazzy, Golden