If the child is 13 he or she probably isn't interested in a slow rc I can help you modify a slow rc like from walmart into a fast one.https://www.instructables.com/id/how-to-supercharge-a-cheap-radio-control/
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1. make it wire controlled. 2 Motors left and right 3 or 4 wheels. Styling is up to you. This might help http://www.tep.org.uk/PDF/NV16/NV16_MechaSocca.pdfTurn either motor off or on with separate switches this allows you to control direction.2. Do the same with a radio control system (bought) or robbed from a toy and set the servo to do the switching.3. Go to microprocessor control - EG the Picaxe will read and act on either IR signals or the output of a standard radio control, system.4. Buy RC system 1 servo and ESC - Servo steers ESC controls speed.The rest of the styling and or mechanicals is up to your ability, budget, access to suitable materials.
Here's an instructable for making an rc car. A remote control car needs certain parts to function, and I'm not sure this is your idea of "simple", but take a look anyways. I'm sure you can improve on the appearance of the project.