More than likely the floor has a polyurethane finish or perhaps varnish.
Do not use any product with water. We use a product made by Bruce for Bruce
flooring that works well and won't harm the floor. You can find it anywhere
wood flooring is sold, like Home Depot, Lowes, etc. We've used it for years.
As for marble, I've used this stuff called Weiman Granite Cleaner, but I don't feel like it's anything special, so I'm curious what recommendations you get. There is another one called Hope's Perfect Granite Cleaner that seems to be getting good reviews on Amazon...
Regardless what cleaner you use, I think the key to granite is to buff it dry with an MF towel to avoid spots.
With the marble be careful of acidic food and cleaner. They can 'etch' the marble and dull the gloss. If you spill citrus or tomato, or anything else acidic, wipe it up right away. And vinegar is a good cleaner for a lot of surfaces, but keep it away from your marble.
I've had marble for three or four years now and I usually use just dish soap and water (just a drop of soap in a pint glass). It works well. For tough, dried on stuff I'll just wet a paper towel or sponge and lay it over the problem area. That will soften up whatever is there so I can just wipe it away; just leave it for 20 minutes (or whenever you remember and come back to it).
Mr. Clean works well, too. I keep a diluted spray bottle of it under the sink that gets used on the counters pretty frequently.
So far I have no stains, discoloration, or etching. But YMMV, and I'd test a new cleaner someplace inconspicuous, like the underside or where you keep an appliance, before putting it into use.