Taking baby swimming for the first time - help 😬

I’ve booked a swimming class for my 11 week old tomorrow afternoon (it’s a private facility via water ducks).

I’m just wondering if I should shower baby straight after swimming or just rinse him off there and give him a proper bath once home? He’s never been in the shower before and I usually just bathe him in his shnuggle.

I know I need to take swim nappies, I picked these up today, and a towel but do I need anything else? Baby wash? Shampoo? The class has already said there is a outer nappy and warming mat which I can borrow.

Do I need anything extra or different for myself that I ordinarily might not take? And do you recommend putting the swim nappy on before we go or putting it on when I undress him there?

Sorry for the million questions - nervous (but excited) FTM!