First, use a Swiffer wet mop to clean and follow up with a steam mop.

I have a microfiber mop system and I make my own cleaning solutions. I’m wondering if vinegar is safe to use as an ingredient. Are any of these travertine tiles, and how do I know?

Looks like porcelain tile to me....tough as nails....but don;t drop your hammer, may crack a tile.

Use whatever you want....but I would caution about using stuff like vinegar and that may not be good for the grout.....but the grout may be mixed with epoxy....in which case it wouldn't matter.Use 409...ammonia...simple green...lysol....Dawn dish detergent....whatever cleans up the mess.