While you can use a hardwood floor cleaner on any type of floor, it will only be effective on hardwood. It won't really help on carpet, and in some cases may damage the carpet.
Custom Building Products has a StoneSpecific line that will give you anything you might need. They are available at all Home Depots and are a fairly good price....
PLain water, mop or rag wrung nearly dry. Murphy's is bad for hardwood. Some people use "Old English" in matching color to take care of scratches, but should be plain water or very, very mild...