Very nice stuff.
I would first start by using wiring up H-bridge motor ICs (they can handle the motor currents right?), with one for each motor and connect them to the dev board, and simply program the dev board to make the robot spin in a circle on the spot for a set amount of time, stop, and then start spinning in the opposite direction and have it keep repeating this. After that you probably know how to control the motors.
Or, if you want to connect one relay with each motor and connect the relay control to the dev board and make it go continusouly turn left for a bit and then continuously turn right for a bit and then repeat (you don't have enough relays for reverse direction). This way you can get the motor to either turn, go forward, or not move at all and learn how to control the motors.
H-bridge is best since your robot can move backwards too, but I don't know if your relay or H-bridge can handle the motor's current since you didn't give any info about that. But you probably know.
THen I would start connecting sensors to the dev board.