I use an EVX 3014 RC ESC (BEC provides 5V & 1.5amps) and I'm worried that to much of the current will be drawn to the motors that not enough of it will be available to the raspberry pi computer (Rev 1 Model B) on board the car. Will the ESC provide enough power through the BEC to the pi at all speeds, if not how can I give the pi a secure power supply?
This is not what you want to hear, I think, but the way to do it is to provide 2 power supplies - one for the pi, one for the motors. The pi supply will not need to provide much current, so it can be smaller and cheaper than the motor supply.
As a bonus, should you decide to upgrade to more power motors which require a different voltage, you're already set for the pi.