The insulation will probably let you get more use out of that room. Usually fiberglass between the rafters works pretty well.
You have to leave some space between the top of the fiberglass and the underside of the roof so that moisture can escape in that air space. They make plastic baffles that keep this space open even if the insulation is too high or gets disturbed - good insurance. There also has to be some ventilation at the top and bottom so air can flow in from outside at the bottom, flow up the space between the rafters, and out again from the top.
The vapor barrier depends on the local climate. There are some differences of opinion on this subject, but if you're calling it a three season room, I am going to guess you're in a climate with cold dry winters and warm humid summers, and suggest insulation with a vapor barrier, installed with the vapor barrier down.