Laying it all out there

[MrForbes]

You should buy two more CIM motors and use them in the drivetrain, and also don't use casters, they make your robot pretty hard to control. If you want to collect balls in the U opening, it should be as wide as possible, to make it relatively easy to do, that means you want a "wide" robot. A 4 wheel skid steer "wide" robot drives pretty well, it can turn easily. But it is kind of "tippy" front to back, so you'd need to keep the weight centered down low, and it sounds like your ball lifting idea would end up being kind of heavy up high on the robot.

You might see if you could use a roller to help collect balls, and a single belt to lift them (see videos by falconmaster on youtube).

You can probably get by with a single motor/wheel shooter, have the ball go over the wheel, that will give it backspin and make it more likely to land in the basket. One FP motor is sufficient, and you probably want a single stage of gear reduction...see if you can modify the plastic FP gearbox to do this. We've done it by just using the first plastic gear stuck in a box we made ourselves, but without some machining help it would be pretty difficult. See if you can find any kind of machine shop that might help you