NiCD/ NIMH + brushed motor = big fun for small money
You are in a wonderful position if you want to upgrade to a very fast electric system, but don't need state of the art.
Currently everybody is switching all their batterys and charging systems over to lipo, so you can find some great nimh batteries, and battery chargers on ebay for cheap.
This effect has also carried over to speed controllers in a way that will be great for you. Everybody is changing to lipo which requires a speed control with lipo cutoff, therefore they are literally throwing away great speed controllers that are no longer great for lipo or brushless applications.
Novak and tekin speed controllers which are smooth and can handle almost unlimited motors are available for 1/10th of what they cost, and they still work perfectly. I would get a novak 410M1c or similar speed control, and speedworks 12 turn motor. your car will burn off its tires, or do wheelies, and it wont cost you too much because the good parts from yesterday are now very cheap.
there is a novak 610RV on ebay right now for $1. this will handle almost any nimh or nicd battery/motor combo that you want.
There is also a speedworks 12turn double motor on ebay for $4.
you are going to be shopping for "vintage rc electronics" but if you get the right stuff it is very very fast.
Those of us who must have lipo and brushless will pay more for our fun than you will.
enjoy