Unless it’s timber frame you won’t need a vapour barrier on the walls, but it’s a good idea to fit one on the ceiling.
As for what insulation type: As space is a premium, you’d want to go PIR, such as Kingspan as it has a better thermal conductivity than mineral wool.
The trouble with insulating a single-leaf wall is you want to create a cavity so if any moisture does work it’s way through the brickwork it drips down the cavity and is caught by a cavity tray, which can then be drained by weepholes through the perpends in the brickwork. Of course, this will lose you space in the room, but British Gypsum do independent wall lining systems for this.
Failing that, an insulated plasterboard, such as Kingspan K118 would probably do the trick.