Stay away from any car that has roll up windows and is registered as less than 1968 or so. The early cars had sliding windows. Most of the cars are very similar, they did not do a lot of changes till around 1968 to 69. Then, seats started changing, but the engine and transmissions stayed about the same. I would suggest you look for a 1275cc engine. The power is fun. Originality in old minis is not as important as with other cars. Unless you buy a Cooper S. Then you are talking money. My car is faster than a Cooper S but worth a third of the value.
Look for rust in the floorboards. there is a front frame , rear frame, but the car body attaches the two. Can be repaired but is a lot of work.