It varies by gym.

Ask the coach/trainer/owner...

In some gyms you need (almost) nothing special (to start).

My gym for instance provides gloves and handwraps. They let you work out in the ring without shoes if you don't have mat shoes.

Another that I called requires you to own handwraps but sells them.

Eventually you will (likely) want hand wraps, mat shoes, and gloves (probably 16 oz bag or sparring gloves) -- but you can find out all of that at YOUR gym.

You can maybe even buy them there, or get advice on how to avoid buying something too expensive or too cheap to be anything but junk.

I bought hand wraps right away because it is better than wearing wraps sweated on by a dozen other people. Then I bought shoes for the ring. Next purchase is gloves, but I am waiting since they do disinfect and blow dry all the gloves after each practice.