Teetosugars, two layers of plasterboard is often used as “fireproofing” and will give a considerable amount of soundproofing on its own.
The bottom line really is with you deciding how “posh” you want the result to be ?
If it’s just a “bike fettlery” and you want to “pump out some choonz” whilst you avoid gardening/housework. Then slap on one layer of 12mm Plasterboard BUT mark the joist centres across the boards/on the walls.
Then, if the sound proofing isn’t what you’d hoped you can stick another layer on at 90degrees.
If you want a proper posh downstairs Den, then tidy up the wiring to maximise the space and follow Trail Rats’ advice by battening out, cutting the plasterboard and slinging in ordinary insulation (wear gloves ‘cos that stuff can be a royal PITA).
Budget job = done in a couple of hours
Posh Den = weekender