Grab for as much hight as you can; at least 12 feet is what I’d want.
About the dimensions of your future space:
While your needs are modest right NOW, think ahead to what other possible future uses you might have for the space, and build in the amount of room needed to shoot and accommodate those projects.
Right now you probably just have single-person presentations, but you may find a future need to use the studio for a teleconference or video conference, or press conference, say, with a panel of maybe three people at a table… or your bosses may decide at some point that they want to shoot 2-person discussions of a topic in a chat show format. Or maybe you have a product that could take a lot of space to show…. try to imagine the biggest thing you’re ever likely to have to shoot, and anticipate future needs. Plan a space to store set materials, furniture like chairs and a desk or demonstrator’s podium or column, and bulky things like jibs or cranes, or just a place to put light and mic stands, wheeled carts, and rolled-up backdrops.
For a green screen studio, depth of the set is often more critical than width. You want enough room to not just put the presenter far enough away from the green or white limbo wall to kill shadows and spill, ( at least twice the height of the presenter for stand-off distance from the wall, is my rule of thumb) but to still be able to move the camera back far enough from THAT point, to get a full-body shot, frame the green/white wall, AND have some good depth of field control between the wall and the presenter.
I think we’ve already had a discussion about your gym noise problems in previous posts, or maybe that was another poster with that problem. In your new space, you will want to build double walls of heavy gypsum board, packed inside with dense insulation, with the inner studio wall acoustically de-coupled from the floor, ceiling, and other walls, using viscous rubbery gasket-type materials, and flexible caulk and glue used for assembly, instead of nails and screws, which become vibration conduits. The inside wall can use carpet tile or acoustic ceiling tile/batting glued on the walls, as a less expensive alternative to acoustic foam wedges.
The floor can be treated with rubber matting underneath and carpet tile on top, or for a serious sound floor, the joist boards can be isolated form the concrete floor using rubbery stand-offs called “u-boats”. The ceiling should use high-absorption acoustic panels, and your air conditioning ducts will need special treatment in how they are hung, attached, baffled, and insulated. Doors should be solid material with gasketed edges, and any studio windows should be double-paned, angled, and/or treated with heavy curtains.