Try apple cider vinegar- you can use it for mirrors, windows, and countertops. You can use baking soda to get dirt and smells out of just about anything- if you have just moved into your home, you may want to make a thick paste of baking soda and water, and slather it onto your floors (don't let it dry) and scrub. This may take you a while, but you will probably only have to do it once and your floors will remain dirt-free with regular upkeep.

I don't know how well you take to dust, but try using dryer sheets instead of a feather duster or costly dusting sheets. Feather dusters work pretty well, but eventually they just move dust around- using dryer sheets picks up the dirt and they're disposable; no muss no fuss.