With the snap together model cars it is relatively easy to remove all the interior parts and only assemble the base, the wheels and axles and the outside shell. Make sure the wheels and axles are working well and turn freely. Experiment with assembling the car using the minimum number of interior parts, you will need that space to work with.
For the lights on top of the car, take the outer shell of the car and drill 6 holes in the roof in a line. Use a drill press and a drill bit with a guage slightly less than than the size of the LEDs. Make sure to use mineral oil or another lubricant while drilling because the soft plastic heats up and starts to melt very fast. Clean the drill holes of excess plastic and then widen the holes a tiny bit by hand using the drill bit. Make sure the LEDs fit in tightly.
Take the base of the car and make sure your Arduino can fit comforably. At this point you will need to consider the location for your motor and how you will connect the axle to the motor. Our very kind machinist designed a pulley system for our axle and motor. We cut a section out of the base to allow room for the pulley around the axle and set the motor behind the Arduino between the back wheels. Make sure to leave room for a couple batteries because your ardunio and all the other components need a power source. You may have to lift the body a bit.