Car appreciation... the aesthetics, the engineering, etc

This looks nice, but I imagine any problems would be catastrophically expensive to fix, no?

Depends if you want to fix it yourself. In the grand scheme of things, most cars are expensive to fix. In my experience, the cheapest parts are on Japanese cars, if you really wanted to go budget, you'd be amazed at how much you can fit in a Nissan Micra, and how fucking cheap they are to run. Likewise with the Honda Jazz. Both are renowned for their reliability.

With regards to that BMW, shit can go wrong and unfortunately, no matter how well some cars have been kept, they still develop faults. BMW parts will be more expensive to buy too but choosing the right garage/mechanic should mean you're not charged more labour just because of the brand.

One of the problems with 15-20 year old cars is that parts that are not considered "consumables" start need replacing. Tie rods, steering arms, wishbones, ball joints, shock absorbers, bushes. Not all of them and not on every car, but older cars need more regular maintenance purely because they're getting old. Not all of these things are essential and not all will be MOT failures, but they'll make everything seem more wishy-washy and detract from the drive. One of the many problems with this is that in the UK, 15-20 winters will have chewed everything to shit. The underside of the car will be corroded and seized so that will make replacing all of these fairly simple and cheap steering and suspension parts, a really long job involving grinders, blowtorches, air tools, really long breaker bars and preferably a 4 poster ramp.

TL;DR

my BMW suggestion isn't necessarily a good idea, buy a Honda Jazz