Cleaning with water probably won't remove the odors. If you have some vinegar or bleach at home, you can use a very low concentration of each to spray the cage down, wipe up with a towel, and let completely air dry (where you can't smell bleach or vinegar) before putting your beardies back in. I most recently started to use a non-toxic, green cleaning agent that's concentrated. If you use a cleaning agent to clean your tanks it'll remove the smell and also the bacteria which will build up.
I have used reptile carpet since Darwin was 6" when I got him, and as long as you're careful picking them up, then there's probably little risk of them pulling out a nail. Can't comment on tile since I don't use it, but it seems like it would be a little hard for jumpy babies.