Much depends on exactly what you will use to insulate the basement walls, how the insulation will be applied, and what type of finish you will install, if any. Without knowing those things, it's not possible to comment except to say that generally, wherever there is insulation, there should be a vapor retarder, located on the winter warm side of the wall assembly.
You should try to determine whether all the humidity comes from the air, or whether there is dampness entering through the construction. You can do this by taping a piece of plastic film to the wall and to the floor. Wait a day, and see if there is any moisture present between the film and the floor or wall surface. If there is, and you don't want to excavate outside and correctly seal and waterproof the walls and backfill with pea gravel or crushed stone, then no matter what you select as insulation, you should be certain the space between it and the walls is fully ventilated, to avoid mold issues.
Basements don't create moisture; it comes from somewhere. In your climate, it could possibly be the air, or it could be entering through the walls, if not properly dampproofed, or through the floor if a vapor retarder was not correctly installed beneath it. You will want to know the answer before you begin to insulate, because it could affect what choices you make when doing so.
Architect (NY) and Home Designer (PA)