I'm sorry if this question comes off as super-noobish but since I can't even tread water for more than 5 min yet, I'd rather be safe than sorry before getting a tail. (I'm taking swimming lessons)

Also I'm sorry again if this question has been asked before (If it was I'd love to be directed to it and what not)

For me, I only really plan to be in a fabric tail. Maybe in the future a silicone tail, but all I really want is to swim in a Fin Fun tail. They always have younger kids who can swim really well.

Plus, I only really use the public pool or my family friends' (who live far) pool so swimming too often isn't entirely possible LOL.
I know the dolphin kick is really important but what other basic swimming abilities should I be able to do before I get a tail? I've read that you should be able to tread, and generally be a strong swimmer as well as the dolphin kick, but what other things should I remember before swimming? Should I exercise my core?

Thanks!