If you really need to cheap out on it, you can remove the wireless chip from an existing RC car and take over the H bridge inputs, or even just tap into the ant

If you really need to cheap out on it, you can remove the wireless chip from an existing RC car and take over the H bridge inputs, or even just tap into the antenna input pin and inject serialized commands. Most low-end 27MHz toy RC sets use clones of a well known chipset called RealTek TX2/RX2, and there are Arduino libraries for it. It only takes binary on/off commands for forward/back/left/right/"turbo" at 1Hz or so, which is fun enough for most purposes.