A 12' has plenty of room for 3 people and gear for an overnight trip. I have a 12' NRS Otter that I really like. I think I paid a little over 1k for it new, but I know they've gotten a lot more expensive in the last couple years.
As far as whitewater, a 14' is going to have bigger tubes and be more survivable, but a 12' is lighter and more maneuverable. I much prefer the small boat because I think it's a lot more fun, but I know a lot of people like the comfort factor of the bigger boat.