This is personal and sensible choice philcal,
You can as you say batten out fill with insulation, vapour check and board then skim.
You could batten out, use thermaline or K18 etc... then board and skim (no need to vapour check this as insulation backing of the board already has this property.
You could also consider dot'n'dabbing the thermaline type of boards to the wall, then using a second mechanical fixing
nailable plugs to secure.
If I was intending to fit a gym in the garage, I would take in to consideration wall mount racks and equipment. This as you will know, wants to be fixed very securely to the walls, so I would make provisions for that.
So maybe the best option on at least the walls where equipment could/would be mounted, is to fix very secure studs that are well bolted back in to the wall. Plan this as fixing points for equipment.
As plasterboard will not on it's own offer a good secure fix for very heavy duty equipment such as you would find in a gym.
Hope this helps.
Also electric cable sizes has to be calculated when routed through thermal insulated walls, so if you intend to have electric cables within the walls they need to be rated and fused correctly.
For example 2.5mm twin and earth cable routed through insulated walls can be effected by the insulation at a rate of 50%, thus losing 50% of it's safe current carrying capacity.
If you have any further question regarding this, please do so.