Any public performance of a copyrighted work requires payment of royalties. No real good way around it, even doing the performance for free. Music in particular can be expensive, unless you are doing works old enough to be in the public domain. Cabaret style shows usually include music from a number of different sources, requiring a lot more work to put together the rights and keep the show legal. On the other hand, parody songs are considered fair use and don't require royalty payments.

Royalties for plays are usually cheaper, especially for small houses. Readers theater type shows might be a good way to start off while explore the musical cabaret concept.