You have two general options. One would be to just load up batts on the floor and make sure there is venting in the space. That's cheap and easy, saves on heating costs, but you lose use of the attic. You can alternatively insulate the walls and ceiling, then use the room for storage.
The better solution would be to insulate and finish it off. For that there are a couple of important points:
- Make sure you don't have insulation in the floor.
- Make sure there's a ridge vent in the roof and soffet vents, as well as space next to the roof. (One can buy cheap styrofoam panels to achive that, if desired.) The basic idea is that the wood in the roof needs venting so that moisture doesn't get trapped in there and rot it. A little research should make that all clear. The general design of a cathedral ceiling is that hot air rises out through the ridge vent, pulling fresh air in through the soffet vents, providing a flow between the roof structure and the back of the insulation.
Once you've taken care of the venting, insulate ceiling and walls, add a vapor barrier, and drywall it.
I'm assuming you don't have any horizontal bracing and that there are just low kneewalls on the sides. If there is bracing it needs to stay. Drywall around it.
If the sidewalls are low kneewalls, it might make sense to move in your finish walls and leave room in the eaves for storage.
And what about skylights? You probably want to add some window area and improve venting of the living space. That's something to plan before closing it up. (A note for maximizing skylight benefit: If you frame a 4" depth around the top and bottom of the skylight you can graduate that up to the 6" or 8" roof depth for a better look and more light. It's hard to explain. If you look at a typical skylight you'll see it's set deeply into the roof framing. The glass may be
8" or more from the ceiling plane. Imagine that inset as a cardboard box. What I'm suggesting is to "fold out the top and bottom flaps" of the box for a larger opening on the ceiling side.)
However you do it all, just remember that you want insulation behind the living space and free air flow behind that. Vapor barrier is certainly a good idea. It will help by retaining humidity in the winter. It will also be required by some codes. But don't use fiberglass with foil facing to get a barrier. Staple plastic around the entire interior for a good seal.
Another issue is building permits. Do you plan to get a permit? Is there a local building commision? In a typical old New England house there could be lots of issues that an inspector is not willing to grandfather in: Narrow stairway up to the attic, insufficient window surface, etc. Before you decide to get a permit, make sure there aren't any problems like that.