YOU KNOW that within the limits of your budget, pretty much anything built 30 to 50 years ago is out of the equation. No decent MGB now costs under $20,000 and even Mini Mokes in fairly ordinary condition cost more.
There are cars that fit though, and do it easily, but they are from the later-model contingent, made during the first decade of this century in Europe or Japan. Most will be loaded with fancy features, and performance ranging from decent to dynamic.
They all come with advanced chassis design, great brakes and grippy tyres. Plus, they have convertible roofs which, unless someone has poked a hole in them, don’t leak.
The downsides tokeep amateur tinkerers well away from anything carrying voltage and mechanical complexities that challenge all but the most specialised of technicians.