Hey Pascal,
many build an enclosure from thin plywood birch, which results in something that vibrates like a guitar or piano body, i.e. you prevent a little airborne sound when it’s tight, but it vibrates and makes spread sound anyway. The best solution, as for speaker cabinets, is to use MDF panels as thick as possible, but then that’s a pretty bulky thing, and to take care to seal it completely.
But besides using an enclosure and perhaps soundproofing material that absorbs mainly airborne sound, the best sound decoupling is that of structure-borne sound, which would be by preventing a separate inner enclosure from having a resonant bridge to the outer one. I say this because I have been studying how a table or an enclosure can also prevent structure-borne sound, that is, the vibrations that do not come directly through the air, but go into the floor and into the building.
By the way, what I find important in an enclosure is that the door and the top of the enclosure is not in the way when you lean over the worksurface to do your clamping. I like this one, but not for noise reduction. The main purpose of a CNC enclosure is protection from flying debris of broken bits, which can be very dangerous.
But that is just a thought. I hope others contribute their experience, as I’m still not ready with my enclosure plan.