First project, building a RC-car

You probably won't be able to make just one single purchase and be on your way. Things often come up that you weren't able to anticipate. So don't worry if that happens. The motor shield says it will power 4 motors, the car has 4 motors. You still need external power for the shield. So a battery pack would be good. The Arduino has 6 analog I/O pins. So you will only need the one board. Also, don't rely on pics. Always look at data sheets if available or any other info they may have provided in addition, or in lieu of.