Subpanel for addition

Hi, I'm new here. I've got a question about wiring a new addition to our home. Although I'm an electrical engineer, I'm not up on the wiring codes so I'm hoping someone can point me in the right direction.

Our addition is a new room above our garage. It is about a 75 foot run from the service entrance in the basement. I have 6 blanks left in the main panel. So, I am considering putting in a subpanel (in the closet of the addition). My question regards the type of wire and any requirements for the run to the subpanel. The easiest route would be from the basement up through an interior wall to the attic (one floor), and then across the attic directly to the new room (second floor). Can entrance type cable be used for this and are there requirements for protection as it goes up the interior wall from basement to attic?

I have to run two 20A wall circuits, an overhead light circuit, a 208/230 circuit for a heat pump, and another 20A circuit for a supplemental resistive baseboard heater. A 60 to 100 Amp panel should be sufficient. I think the current entrance is around 200A (house built in 1991 so it's relatively modern).

Thanks for any input,

Jim, Utica NY