Try the classes out before investing in the correct footwear. When starting out, for tap, latin and ballroom and flamenco, a hard sole shoe is fine to begin with.
Ballet can be done in socks/bare feet at the students own risk, until you decide/want to buy ballet shoes.
Trainers are suitable for JAZZ, ZUMBA, STREET DANCE, BOLLYWOOD and FITNESS CLASS. To get more specific advise, please ask the teacher after the class and they will advise.