I chose to insulate with blown cellulose instead of fiberglass batts. I covered
the exposed studs with a non-woven fabric, similar to fabric interfacing, which
let me blow in the cellulose insulation before I put up the drywall.
Another technique is to drywall first, bore holes for the blower hose, fill and
then patch the holes. Doing it that way, however, you run the risk of popping the
drywall off the studs.
Insulating with cellulose is more work than fiberglass, but after researching both,
I concluded that cellulose was a better choice.