Honestly, Iceman, I've been teaching in a Y for over 10 years - my class meets in one room on Mondays and a different room on Thursdays, and just to complicate matters, the 2 rooms are in buildings on opposite ends of the parking lot, about a block apart. Many of the things mentioned are nice to have, but none of them, even the things I suggested, are truly necessary. A clean, bare floor - which is what I started with - is really the only thing you truly need. Any of the other items listed that you can reasonably store and access in a timely fashion are nice to have.
We do sweep the floor before class - but the Y has plenty of equipment, we use their dust mop, because all the other classes wear shoes - so we don't own one of our own.
I definitely second the first aid kit; I have one I carry in my gym bag because we rotate rooms, and I didn't think to list it. The Y has a first aid kit, but all it has it in is band-aids, at least at the Y I'm at, so I also keep chemical ice packs in both rooms; they're too bulky to carry around in any quantity.
We do sweep the floor before class - but the Y has plenty of equipment, we use their dust mop, because all the other classes wear shoes - so we don't own one of our own.
I definitely second the first aid kit; I have one I carry in my gym bag because we rotate rooms, and I didn't think to list it. The Y has a first aid kit, but all it has it in is band-aids, at least at the Y I'm at, so I also keep chemical ice packs in both rooms; they're too bulky to carry around in any quantity.