You could buy an old Volkswagen bug (not the new models) for cheap. They are dead simple too with tons of parts available.
Depending on where you live you can almost build certain older cars from new parts. For the UK I believe you can get every single part of an Morris Mini either brand new or at least refurbished. For France you can probably built a Citroen 2CV for parts, including an EV version.
A friend is doing exactly that with a defender 130 . New galvanized frame, every panel new, new axles, new brakes, new transmission, transfer case and engine. New seats, new interior, new doors. Cool project.