basement partition walls

I am re-finishing the basement a previous HO started, and am removing the wood paneling and installing moisture resistant drywall instead. I have some partition walls separating the living space from the basement space and was wondering if I should use moisture resistant drywall on that too or if i am ok just using normal rock? Basement is mostly water-tight but there is a little moisture here and there (working on remediating that too). I just don't want to regret anything down the road, but don't want to spend money unnecessarily if I can avoid it (which is why I'm doing the work myself).

Also, would you insulate the wall too? Foam board cut into the spaces or bats?

Thanks.