I can't recall any details in a book that conclusively say one way or the other (yes, I *am* going to re-read them but there is the matter of borrowing them ;)). I thought at first they were chosen, as part of the "becoming an animagus" process, but now I'm not so sure. Perhaps the form you take reflects something of your personality. It's possible that Rita Skeeter didn't become an insect animagus because she was a journalist, but the other way around.
What would that mean, if the animal form wasn't something you got to choose? Someone could spend a few years becoming an animagus only to discover their alternate form was.... a lizard. Or something boring. But perhaps it wouldn't be boring *to them*, and that's part of the magic. Only the kind of person who will get use out of turning into a rat actually has a rat as his animagus form.
I wonder if there is a spell or something to see what form you would take? Why aren't there more animagi?