Music Lover
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I would finish the walls a plastic vapor barrier studs and then cover with sheet rock. For the floor, if you are concerned about humidity, I would put a plastic vapor barrier down and lay tongue and group plywood over 2 x 4 studs. You can screw the plywood down onto the studs. The weight of the plywood will keep the studs from moving. After that you can put whatever flooring you want (carpet, ceramic tiles, wood flooring).
If there's a concern about moisture then a plastic barrier will trap the moisture likely possibly to mold. I would use Dricore panels instead as that provides separation and room for air movement to keep things dry.
FYI...my friend put down 2x4's and plywood. It moves in a couple places. Unless the floor is perfectly flat there will be spots where the 2x4's don't touch and there will be up and down movement. That also applies to Dricore panels on an uneven floor. That may or may not be an issue for people.
Another option is to lay down a plastic dimple underlayment and then screw down T&G plywood into the concrete. It's a lot more work but guarantees an air space, stops flexing and maximizes head room.
All these suggestions are made not knowing the circumstances of the OP's basement. It might be perfectly dry with no moisture issues at all, and in that case carpet can work.