You're gonna need a car ~£500 and an engine at about the same if not more.
My guess would be you would need the t-jet gear box, ecu and all ancillaries, which can add up to a surprising amount of money to buy. would would likely need custom drive shafts, uprated brakes and uprated suspension all round.
you would need custom engine mounts, exhaust and may need to replace things that you've not thought about like the switch gear in the car, fuse boxes and wiring to get everything working and in tune.
Long gone are the days where you would just weld a bracket and fit any different engine to any car.
Essentially all you would keep is the shell and seat and steering wheel.
there is no point not doing the suspension and the brakes because you want to use it on a track so it needs to slow and go round corners.
you can buy a punto grande T jet on Ebay right now for £1800. Far easier and more cost effective to buy that,, and strip off every ounce of weight that isn't needed.