We're doing spray foam in the vaulted portions (adding a shed dormer as well).

Here's what we did with a west-facing sunroom addition we built a couple years ago. We have a cathedral ceiling, so a little more space than vaulted, but the same principles apply.

We nailed 1 1/2" foil-faced polyiso board (the blue board with foil on one side) to the rafters. We nailed 2" strips of plywood over the top, as to work best you need air space in between the polyiso and the drywall. We then sprayed cellulose above the polyiso board before closing it all up. We put t&g pine boards over it, not drywall, but you can do either.

The above methodology was courtesy of the illustrious mongo. Here's a work in process photo of a flat ceiling and part of a wall that got drywalled.

The amount and sometimes the type of insulation is usually based on the predicted heat loss/gain of your climate, orientation, shading, the applicable energy code and the venting required. To get good solutions you need to carefully define the design problem.

Thanks for the replies so far. We live in Dallas so we have more hot than cold. (Cold for here, but not compared to other parts of the country). The windows face south, making the roof east/west.

Here is a picture of the room/ceiling that needs insulation:

Picture of front of house. This will look better once the siding is up and the windows are moved up:

We also did the spray polyisocanurate (sp?). It's a "hot roof", right, with no ventilation?
For use, this was the best way to do it, for our climate, for the rafter size, to get the best R-value. it wasn't too expensive, and of course you get the tax incentive with any insulation project anyway...

We did a similar vault. The GC put up bat insulation as shown. It was a "double" ceiling, if you can tell from the first photo showing the framing.

interesting..I was going to say just spray foam the whole thing but doesn't the area have breath or stuff will rot....is the purpose of the 1x2s of the foil foam stuff...?