The shoes, your instruments, are important. No Maryjanes, patent leather (i.e. plastic), or folk-strap shoes.

Each dancer needs a well fitting pair of leather tap oxfords, which are lace-up unisex style shoes. There are four good brands: Capezio, Leo, and Bloch and So Danca, each with different sizing systems, so go by fit not size number. The shoes should fit perfectly in length, and have tongue showing under the laces to allow for stretch in width. If you are a beginner get a softer shoe so that your arches are strengthened by working them. As you advance to intermediate level a harder shoe will then work with and for you.