If it's a common show, then Joseph Weinberger and Samuel French are the places to start - they are probably the two who hold the rights to all the popular plays and musics. A few shows do it themselves.
Just be aware it can be complex and there may be very strict rules on audience, money, and what you can and cannot do. If it's a musical, then there will also be hire charges for all the sheet music, and some even restrict you from editing anything - Most, however, just involve filling in a form, and paying some money. You can normally get perusal copies to have a read through.
A musical for your first production is a bit adventurous - do you have the other critical people in your team? Choreographer, MD, technical, set and costume? Musicals are multi-player things, a straight play can have a reduced production team, but finding lots of people of like mind you trust can be difficult.