As a first step, try controlling it by bluetooth. Move to home networks later! And, by my view use microcontrollers instead of Arduino. They are much more flexible. Tell me if you need any help in case of Coding or Hardware necessities.
u should go step by step. it will make u experienced. first try to control the car by bluetooth module. then transfer everything to wifi. because using wifi (xigbee) with arduino is pretty complex. u should at least be ready to move the car before introducing xigbee. so use bluetooth module. ask me if u need any help with bluetooth softwares or hardware.