You can use H bridges to get precise control of the motors. You would need 1 H bridge per motor, and you want H bridges that can handle at least 20 amps. You can find a few different H bridges on our website, http://www.progressiveautomations.com/control-systems/plc-controls
. You might get lucky with our WASP motor driver, but that has 10A continuous current, so it would be close. The Scorpion XXL can control 2 motors, each at 20A continuous. That would work better.
As for operating the bot wirelessly, you could try an RC controller. That would work easily for the drive motors, you may even be able to find one that's plug and play with the Scorpion. If it's not plug and play, you can use an Arduino as a brain, and input the receiver signals from the RC controller to the Arduino, process them, then output the control signals to the H briges to drive the motors.
Adding 5 extra channels for the arm could be harder. The easiest way I can think of (though its still not very easy) is to make some sort of bluetooth control and control it with a smart phone. That would be some advanced programming though.
Another way would be use the switches on a RC controller. Most controllers I've seen that have lots (5+) of channels, have a bunch of switches and buttons on the controller. You could use the main joysticks as drive control for the motors, then when you switch a switch the controls change, and now move the arm. This would be easier to program then bluetooth control, but moving the robotic arm intuitively may be more difficult, because you'd be most likely moving one or two motors at a time, rather then the arm as a whole. But that depends how you build the arm.
Either way, I've made a fair bit of assumptions about your project, if you can share more details we can help you further.