Advice for insulating the garage

I have a detached garage that i want to use as a workshop. I want to split it into 3 areas with just the back 2 insulated and the front where the main door is will still just be a little garage.

I think the walls are 2 skin but there's no cavity and it has a pitched roof with tiles, but the joists from wall to wall are a bit thin. The floor is concrete.

I'm thinking of adding more joists on hangers, then i can board the top of those and use for storage without affecting the current roof structure. I could add add some insulation between them before boarding over them.

for the room divisions I'm thinking of building a stud frame attached to the new joists and floor but with an air gap from the walls, insulating in between the studs. I will be making quite a bit of noise so want to try and keep as much in as to not annoy the neighbours.

For the concrete floor, just sticking a damp membrane down, some insulation and then board over.

How does this sound? Is there anything i need to be aware of? I don't intend it to be a proper room with building regs, just somewhere that will be warmer in winter and keep some noise in.