I mopped for a living for years, with attention to the causes and effects.
Don’t use more detergent than you need. Most of 'em are effective at 2 oz. per gal; measure it, no glugging! Any more than that leaves a film. I use Lysol disinfecting detergent, not because of a preference, but because that’s the brand Lowe’s sells.
If you’re a stickler for leaving nothing on the floor, you can do a second mopping with plain water.
My favorite, and stingiest, way is to mix a single gallon of hot water w/ 2 oz. detergent in a pump-up garden sprayer. Mist the floor. By the time you go back with a plain-water mop to pick it up, the chemical has had a few minutes to work.
Before you do your main mopping, “frame” the room with a single pass around the edges.
I’m not fond of bleach. If you like it, help yourself. Don’t forget to protect your skin and eyes.
Thanks again, all, for the replies. I think my biggest problem is that I can’t wring my mop out as well as it needs. So the bucket thingy might work for me. Will also check out the O’Cedar mop. Will still need a wringer bucket for sure.
So, question for Bay Area moppers. I wanna buy an O-Cedar or similar microfiber mop with a wringer/bucket. Checked Target and Bed Bath, they don’t carry it. Don’t want to buy it off Amazon if I can help it. Any other suggestions?
If I really want the floor clean, I fill the mop bucket with hot water and add a capful of pine-sol. Then I get out my floor scrub brush and go to town. Once I’ve scrubbed the floor, I go over it with a clean mop to pick up any water (if the water is clean hot* it should evaporate pretty quickly and you shouldn’t be puddling water on your floor anyway.) that’s left.
I do this like twice a year. The rest of the time it’s a once over with a mop and pine-sol water and most frequently a foot swish with a paper towel.
Use a wet/dry shop vac with the squeegee head. Saturate the floor with soapy water, scrub with mop, slurp it up with the vac. Saturate floor with rinse water, slurp it up. Clean floor, little drying time!!