If this is a single skinned outbuilding, then the air is not your only problem. Bricks wick water through them. Even if you seal the room up, water will get in through the brickwork and even the concrete floor depending on how it was laid. In winter the wall of my garage which is 1 foot away from next doors actually weeps water and has a dark stain of moisture down it. There isn't enough air gap between the two buildings so damp air collects there and rain that gets in doesn't evaporate in any sunlight.
Yeah this is part of my problem. To minimise it I moved soil and greenery back from the outside face of the walls. I then coated the outer face of the bricks with a spray on paving sealer (clear). I really loaded it on to seal the bricks and stop further penetration.
I know that sealing or coating bricks is taboo in the UK. Supposedly bricks are meant to "breath" and if you coat them and trap moisture they are prone to cracking in winter. There was a whole fuss as "cowboy traders" where going door to door offering "damp proofing" armed with demo bricks and spray.
The "Building code" way over here, if you were to register it as an "indoor space" would require vapour barriers with vents and drains on the wall, followed by stud/frame work to hold insulation.
The floor will need the same. I looked into getting my garage to a point where I could use it as a year round workshop, but you can even see daylight through the brickwork in places. The materials alone to membraine it, foot it with treated timber, frame it, insulate it and sheet it was looking at £2500. That wasn't going to include the new door, window seals and a new insulated/sealed garage door.
I ended up leaving it the cob webby "junk room" it was. Electronic devices last about 3-5 years before damp or spider nests kill them.