Vapor Barrier Advice

Since you're going to have the walls open, I would use pre-faced fiberglass batting. The rolls give you more flexibility than the pre-cut batts if you have non-standard height walls and they're usually a little cheaper per square foot, but I see special offers in the big-box stores all the time so shop around.

There's no special trick to installing it, but wear a dust mask that's rated for fiberglass dust. The vapor barrier goes on the warm side. I usually cut pieces to length before installing them in the wall (but I'm an engineer and can't help myself! :), but you can cut it to size while it's in the wall if you're not as OCD as me: put the loose end at the top of the wall, unroll and stuff until you reach the bottom then cut it off. Run a bead of adhesive along the stud, then unfold the flaps at the edge of the insulation on one side of the stud and press into the adhesive. Repeat for the insulation on other side, then staple the two of them into the stud. Tap the staples in with a hammer if they didn't go all the way. Done!

I don't have a book recommendation, but it's easy to learn how to do it.

No, you only want a single vapor barrier. A second vapor barrier would create a moisture trap that would cause more mold issues. If there's a condensation issue, I'd replace the section of HVAC ducts with an insulated duct. The insulation inside the duct prevents the outside metal part of the duct from getting cold enough to result in condensation.