Finishing half of basement, should I insulate all?
You do not have to insulate the part that will be unfinished, but you will need to insulate between the finished space and unfinished space and include an appropriate moisture barrier.  All things being equal, if you don't have moisture problems in the unfinished area now, you are not likely to create them as long as the unfinished space has adequate ventilation.  I will follow that statement with the disclaimer that there are a lot of site specific circumstances that can cause moisture problems whether you insulate it or not.