Unless it is a particularly loved and cherished e36 that you come to buy (which will usually mean that they are higher priced), then it will most likely need a whole host of work doing to it in order to make it both reliable and to bring back the vibrancy of the handling/chassis.
Anyone kidding themselves that a £2k e36 will be anything other than somewhere to spend more money month by month has evidently never owned one or seriously researched one.
That said, I'd still have one, but that is because a) I love how they look b)how they drive, and c) how much I know about them. I'm also handy with a socket set and could pull apart most of an e36 and rebuild it over the course of a long weekend.
As I said, depending on model and year you could easily get a well kept car for that money. It all depends on what went with the previous owner as well.
I don't particularly agree with your anyone kidding themself about a 2k e36, as you said it depends on the owner. And price comes down to engine size and year (and condition obviously).