You need microphones (1+ depending on how many vocals needed), special instrument microphones (1+), a mixing board, computer audio software, microphone stands, music stands, a couch for comfort, a tall stool (some artists perfer to be seated, others chose to stand), head sets, a CLEAN room (I have been in some disgusting studios and walked right out. It’s a major turnoff if where you perform is cluttered or dirty), a water dispenser, paper cups, and other minimal design elements. ALso make sure you have your resume and business cards handy.

As far as sound proofing is concerned – I reccomend locating someone that treats rooms and acoustics. You would most likely need a professional to do the job right. Search around your area and compare prices & check there references & work.

The best of luck to you! I hope this helped
References :
Reccording artist for opera/broadway/children’s music