A Mini can be nothing other than 2nd hand nowadays.

I use mine for commuting (25km) every day.
The hardest part is when you first get it. Every Mini I've gone through
needed a "reliability" phase which lasted a couple of months of ironing out
the little things that the previous owner didn't take care of (brakes,
bushes, electrics...). Once everything is in order and well maintained, you
shouldn't have any trouble.

That budget puts you right in the middle 90's. Cars of this age suffered
from poor build quality. You may find buying an earlier car for less money
will get you a better example. If you do buy a later one, make sure it has
been has some rust treatment carried out (waxoil or similar). If you manage
to find a rust free example, you should budget for a thorough rust proofing.

Mechanically, you should allow for frequent servicing and invest in a grease
gun. Oil and filter changes every 6000 miles for a manual or 3000 miles for
an auto. Grease the suspension at least every 6000 miles.

You have to bear in mind that you may be buying a mid 90's car, but it is a
1950's design.

That said, it will be the most fun you can ever have with your trousers on!