Insulating interior basement walls

Hello,

First, I'd like to apologize for my lack of experience---I'll likely use some incorrect terms.

I just bought my first house and the basement has a partially-finished room that I would like to use for an office. It is wired, vented, and has drywall up with 2 walls being external and 2 being internal. Unfortunately, they failed to insulate the external walls before, so I know I need to do that. My home inspector suggested having loose insulation sprayed rather than taking down the walls.

My question is regarding the two interior walls. Do I need to insulate these from the rest of the unfinished basement? Eventually I would like to finish the entire basement, but it would likely be a year or two before that happens.

Thanks