What would a basic arduino controlling system for an underwater ROV be like?

I am working on an underwater ROV for a competition and have been considering using Arduino to control it.

However.

I have not actually ever used Arduino and therefore have no knowledge of the subject.

So my question is this, what would the basic components be for controlling the ROV be?
It would have to be able to control several (4-ish) medium sized motors as well as 2-3 small motors and i would LIKE to have either a joystick and a few buttons on the controlling side.

I can imagine ALL the power would be unable to be run through the Arduino system so would it be that there would be some kind of second component for say each motor to control power flow?

Also the motors are "double throw switch" motors so there would not need to be any kind or" throttle "