I found the disposable swim nappies perfectly good and they could be used several times (and washed in the washing machine). I did find it was easier for me in a poo situation as I could just take it off and bin it - whereas the reusable had to be taken home, soaked and washed. Not a huge amount of work, granted, but we were at the pool/beach a lot.
If you do go for a reusable, try to get one with poppered sides as, again in the case of a poo, they are easier to change.
DD was always fine in just a swimming costume over the nappy. She probably didn't need one, but I bought her one as it was cute .
She never wore a wetsuit until she went in the sea, and her first dip was at 13 weeks in an open air pool in Newquay! She was certainly always fine in any pool we went in for a good hour in just a costume. But maybe that's just her, as she is a very hot child who doesn't seem to feel the cold.
I never put her in lessons as I taught her myself, but looking at the ones at our local pool, they did seem to spend time sitting on the side of the pool, which dd never did, and it's then that they get cold, so a wettie might not be a bad idea in that situation.