I have a 200amp main with about 4 to 6 empty slots I wanted to know if that would be enough to finish my 1400 sf basement?
with small kitchen, living area, bedroom, bath and a home studio
and if I need a sub panel what would I need and about how much would it cost?

I'm finishing my basement and I wanted to know what is the best way to sound proof my new studio? It will be a 12 x 12 room with a 4 x 5 vocal booth

You should be fine if you use twin breakers. (2 breakers to fill one slot) Best thing to do is post this in the electrical section so TKRussel can give you the correct answer.

As for the sound proofing, years ago I helped on a recording studio in a guys basement and we used 2x6 studs w/ R25 batt insulation in the walls and ceiling, then 2 layers of 5/8" drywall on the walls and ceiling. Then we hung homosote panels to help absorb the sound. The door he had us install was a solid core door w/ homosote board on it.