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A Midget/Sprite is on my list. My advice is to plan everything out, then install the motor and major components, and buy batteries last. Quality is improving and cost is going down swiftly.

If a Nissan Leaf motor fits, that's what I'd go with. It's one of the cheapest motors you can buy, and it has more torque than the transmission can handle (torque can be easily dialed down). Cheapest way into anything is to buy a wrecked Leaf and use as much as you can.

A lot will come down to your range goals.
 

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You figure the stock Sprite put out maybe 72 ft-lb of torque through a 3.20 first gear, so you're looking at a minimum torque-handling capability of 230 ft-lb for the diff. These aren't fast cars by any means, but if you have first-gear acceleration all the way to top speed instead of 25mph...that is pretty quick. I'd probably just limit torque and drive the car some before committing to a new rear differential.

You may want better brakes for a faster car, but keep in mind that regen can slow the car down quite a bit as well for "free". You might be good with what's there.
 
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