How big is your studio? What kind of studio shots you like to do. I mean, if you have a middle size garage and you want shoot at more thyan one person, you neet a wide angle lens. from the other side if you have a great space you can chose different lenses.
Bascally prime lenses are better, talking about distortion, price and sharpness. But you need to budget 2 or more lens ( my goal is a 35mm, a 50mm and 85mm)
And the most of work in a studio ambient is done by the light. Modifer, flashes, tripods...
But whithout knowing the size of the place where you shoot,i'ts hard to suggest something, in my opinion.