Insulating attic storage space

We’re currently not using this space but want to start storing stuff in here. The door hatch opens up into an office/bedroom.

The floor is floorboards. The previous owner has put down lining paper. There might be some sign of something on the paper at one end?

I was thinking of insulating the wall between the this space and the adjoining room (maybe using insulation boards between the studs?). I’m aware the house needs airflow, and I don’t want to cause any issues.