Get some handwraps and go to a gym. They will probably even have wraps at the gym that you can buy. Same with a mouthpiece. Once you start sparring, the gym will most likely also have head gear and other protective gear. No point in going out and spending a ton of money until you try it out and see if works for you.
Ruben Olivares was 5'3" and Chiquita Gonzalez was 5'1". They did pretty well.