I bet you are a very organized person! I love that you bought different colored rags for cleaning different areas!I have white tiles in the kitchen, a very large foyer and a bathroom. I can't mop floors due to painI ordered a steamer (forget the make) from Walmart and it is very very light. If I didn't like it I knew I could return it to the store and not have to return it by UPS. It is very easy for me to use and the floors come up great.
When I first moved here a year ago (it is Senior Citizen housing) I saw that there was a film of ground in dirt that bothered me that made the floors look dingy. I took a regular mop and put a green scrub pad under it and sprayed "Awesome" that you can buy in the dollar store and I did a few tiles at a time and scrubbed them to come up to a really white. What a difference. I figured that many old people lived here and they really couldn't get to the nitty gritty of deep cleaning that floor and after years they got dingy. It took me days to do because of the pain but I finally completed the task.
Then I went over it with the steamer and the floors came out great. In the laundry room here in my hall way of the building there is a big industrial sink and rolls of paper towels along with washers and dryers. I take the steamer pad and wash it in the sink and then get alot of the moisture out by rolling it inbetween the paper towels and then hang it. That way it doesn't get smeily in between washings. I use the steamer all the time but I plan to deep clean like I explained above once a year to keep the floors white. I never heard of "Awesome" until 3 different people told me it is the best cleaner in the world. I am sure it isn't environmently friendly and I don't have pets or small children so I bought some and I love it. I just used it on the floor though (full strength right out of the bottle with a rinse) but I use other cleaners elsewhere as I think 'Awesome" has too strong of a smell ever though it works great. I buy what is on sale and stock up and play switcharoo. My place doesn't get that dirty as it is only me living here and I have only lived here a year and when I moved in everything was spotless and newly painted, except for the dingy floors that looked white but needed more, sorta like teeth whitening. :-)
I also use antibacterial cloths that only need a small dampness on things like TV screens, computer screens, glass pictures etc. They clean great and leave no streaking. I also use them dish cloths and in the shower. I bought a big packet of 3 different colors and use one color for dishes, one for me and my body and one for cleaning and so far so good. You can't use any type of softener on them in the laundry though as they lose their antibacterial features.