Usually just the Exterior Walls of any basement project are going to be insulated. You are never really insulating interior walls unless you are using the insulation as a “sound barrier”. The exterior walls of the basement include all walls build directly in front of the foundation walls and any wall that boarders an “unfinished” area of the basement such as a storage room.
Unfinished areas will continue to stay cool all year long and so, the new finished ares need to be shielded against this cold spot with an insulation barrier. You use the same insulation type to insulate walls that border unfinished areas as you do with the exterior walls. In Pennsylvania most insulating codes call for R-13 as the minimum R-Value that you can use to properly insulate these walls. There may be a different Energy code for basement finishing in your area of the world, so check with your codes office first before purchasing your insulation!
Make sure you purchase insulation that fits into basement walls that are framed 16 o.c. (on center) and not for walls that are framed 24″ o.c.. Take your time and get this part of the project right. A properly insulated basement will keep your energy cost down year round, not to mention nice and cozy as well!