An ROV offers an entirely different way to use Arduino to explore a new world. This project is a bit different in two ways. First, there is quite a bit of mechanical work to do, and second, it is almost impossible to send wireless signals through water. So, you are going to use a tethered control line to give your robot direction.
There are several possible approaches to building your ROV. Although controlled by a different processor, the mechanical design at openrov.com/page/openrov-2-0 is quite elegant, and you could certainly build the HW yourself and then integrate your Arduino. At openrov.com/page/open-rov-designs-1 is a simpler yet similar design that incorporates Arduino. Another design that is very different from the first one is available at www.instructables.com/id/Underwater-ROV/. Both could certainly use Arduino as the motor control.
My physical design is based more on the latter design that mostly uses plastic piping, as...