You have several considerations here. First, squeaks are caused by sub-floor movement up and down on nails. They're also caused by shifting joists. I'm addressing the same problems in my project. Plywood, OSB, etc., are used for sub-floor,3/4." However you said you have some sub-floor already, correct? I was told 1 1/2" of sub-floor is plenty for any type of flooring. You don't want to go too high! You have doors and molding to consider! The final layer before laying floor is "rosin paper." This will also help prevent new squeaks from starting with new floor. You're going to have to try and tighten up existing sub-floor by driving more screws through it into joists. You can also add "bridges" between the joists to stop them from moving. They're for squeaks over a large area. Lastly, insulate underneath, if you have access. That should cut down on drafts. Good Luck!

OK. Over the weekend I bit the bullet and pulled up the carpet. The plywood subfloor (4'X4' sheets) is in great shape, but because of multiple layers of subflooring the previous owners installed in the kitchen I have a difference of about 1 1/4" - 1 1/2" between the floors in the two rooms. The transitions at the other adjacent rooms are level with the subfloor.

I suppose my only option now is to install another layer of subfloor of sufficient thickness to 'split the differnce' between all adjacent rooms, once the finish floor is installed.

With that said, is there a particular grade of plywood to use? Is CDX recommended? How applicable is MDF for this application?

if you choose a nail down or a glue down floor cdx would be best,with a floating floor any thing will do.check your local home center for possible transitions(t-mould,babythreshold,or reducers) its possible you wont need any more underlayment

Don't use MDF. It is not suited for floors.

There is a plywood pine underlayment that I use in 5/8" thickness. One side is filled and sanded smooth.

To correct some terminology, Your 1" shiplap is your subfloor. The existing plywood over that is your underlayment. You would be adding another underlayment. If this floor is unlikely to see moisture, you could also use particle board for a smooth surface and minor cost savings.

Screw down what you have to the joists and use rosin paper, tarpaper, or glue between the layers to reduce squeeks.