Insulation in the basement underneath of the fireplace

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.

Rather than go to the trouble and expense of tying external insulation from below ground to the siding, I'd let them stop with the below ground insulation. It at least will add a little extra R value.

Then, since your basement is unfinished, but you do use it, I'd go ahead and add additional insulation on the inside of the house* - from the ceiling on down, at least to several feet below the external ground level if not all the way down. (Those extra few feet won't do much on the bottom but they will help some and they won't cost much more...)

*Making sure that any other potential water issues have been dealt with

The key thing with insulation is to get a continuous thermal break. Even a small gap in the insulation can allow huge amounts of energy loss, and since you are running heat downstairs, while I don't know precisely how to calculate the long term savings, there will be one, and more importantly, your basement will be much more comfortable for year round use.