Though you have a proper background and can probably handle anything Arduino-based, start with an Uno first - then move on to something more powerful; the Mega might be a good choice here. I am pretty certain that if the Arduino platform can control a quadcopter - it will be able to handle the needs of your robot.
The only reason I say to start with the Uno is the fact that most example code out there is for the Uno. Also, there are tiny differences between an Uno and a Mega - certain pins are different in function, plus a couple of other tiny issues. You need to start with the base platform, study it well, and get comfortable - and then research what those differences are.
Otherwise, you might find yourself trying out a particular piece of code from the internet, and it not working or something - and tearing your hair out, when it was meant for the Uno - and not the Mega - because of those differences (which the original author or tutorial writer didn't take into account).