I'm building a shed studio too, and I'm having some problems with dampness.
Maybe line inside with osb, and then plasterboard, paint the outside with a sealant paint, and redo the felt roofing(maybe just a 2nd layer over the original).
Will you want to insulate the shed for noise, or is that not a problem? If yeah, then bulk up the shed will osb between the joists, and then build a room within the shed, decoupled from the outer, and fill the void with insulation.
The shed is only 8'x9' so this might not be practical, but i suppose my control room will only be 6 1/2' x 7 1/2', which is probably the size you'd end up with.
Fit a new solid core door, or bulk up the existing with MDF, and add door seals. If you go with the room within the room idea, then install a second door that swings inwards, also with seals.
If you are unsure with what I mean, just ask and I'll draw and post a picture.
Also, what i suggest may be totally wrong, so don't do it until it has been approved by Rick or someone.