I was in charge of cleaning when I was a manager at a studio and I was very conscientious about smell and timing because of the environment being that of a lot of breathing and sweating.
I had a large push broom for the wood floor and many washable white cleaning towels. I also used Clorox bleach tabs in the toilets
I used vinegar , water and lemon for many things and may I add that it’s very important to keep your space clean at all times!
I bought everything at Costco or Target
Check with some of your local gyms for a reference. Since this is NOT really competitive information, and since you may find better pricing and customer service locally, this may be the best way to at least START your search, and local gyms/fitness centers should be willing to help.
I hope that this helps.
there are certainly many, and here is one link: http://www.all-greenjanitorialproducts.com/. What I would focus on are products that are environmentally friendly. You can even make this a marketing point by telling customers that, particularly with reference to a child care center. Parents may not be concerned about themselves but they care about their kids.