Cleaning and Stain Removal - Mopping Floors

I live in a big old brownstone that we just bought last year. After initially cleaning the floors on hands and knees, I have been using a Swiffer wetjet. But I noticed that a few days later my floors are filthy again. We have not changed any of the flooring yet so it is a mix and match of old linoleum (and I mean old) peel and stick tile and parkay flooring. Until we can pull it all up to reveal the nice pine flooring underneath, I have to clean it. Swiffer is not working and my knees are a wreck for days even with using knee pads. Does anyone use a type of mop or mop/cleanser combination that they swear by? i.e do you use a bee-mop and vinegar to get the best results?

sounds like to me the swifer system is either using a high pH cleaner which is leaving a residue or softening any polish or was that was put down on the floor

8 0z of vinegar/gal of warm water is good

or a good neutral pH cleaner in Cool water will work as well.

I have the Hoover Floormate Hard Floor Cleaner and I swear by it. I have a tile floor with light colored grout and hard wood floors and it does great on both. I couldn't even believe how dirty the water is after I use it. It's kind of expensive but I really like the product.