I discovered the microfiber method when doing research on cleaning strategies for my church. It was developed for hospitals, laboratories and other places that have to control biological contamination, and it's said to get over ninety-five percent of the dirt and germs where traditional chemical and cotton cleaning gets only sixty or seventy percent of them. So far, that claim seems born out both at the church and in my limited experience around my house. It works only for hard surfaces, of course, not on rugs.
I got several plastic spray bottles, one quart each, from a cleaning supplies store. I put hot water in one of them for general cleaning. I no longer use glass cleaner on windows or mirrors, the water and microfiber way works better. When I especially need to kill germs, I use another spray bottle filled with hydrogen peroxide. I have a third with white vinegar in it to attack odors. Even on the bathroom floors and kitchen counters, though, plain water seems to do the job most of the time. Just be sure to keep changing to a fresh, clean rag whenever one gets dirty. It works by mechanically cutting off the dirt with all those microscopic threads, and so it only picks it up, it doesn't dissolve or neutralize it.