You don't have to rent an SUV, but it will help. They have the airport ski shuttles that will take you up there directly from DIA.
If you do that, I would suggest staying in town in either of those places (Breck or Vail) so that its easier to get around to restaurants, bars, rental places, etc.
I have never really stayed up there before, always just day trips for me or stayed with others...maybe some others here have ideas of places to stay. A lot of it depends on how much you are willing to spend.