A useful size might be something like 17x15x8. Square rooms will have issues with standing waves, especially a room 16x16x8.
As far as a dual purpose room goes, it's going to be difficult to achieve both things simultaneously and get good results with both. A recording studio, especially a project studio like the one it sounds like you're proposing, is a fundamentally different environment than a home theater room. Aside from the need for isolation, the actual acoustics of the room are very different. That, and sharing a dedicated theater with a mixing board and such will be difficult.
Also, since this is a new room you're building, there is much to be considered for HVAC, lighting, electrical, flooring, floor isolation, ceiling isolation, and other stuff.
But above all, you need a budget. What is your budget?