On your question about drips and sprays, if you grout over the entire tile it will fill in the voids, if any, but the key is to use a very good penetrating sealer. They tend to be very pricey, but they are very effective. Most are about $100-$200 per gallon. In your case about a dixie cup full will do your bathroom in it's entirety.
As for your second question on the 4x4 tiles in the shower floor, you can use them if the shower floor is large and the slope is very gradual. The floor also needs to be very level with a slight slope. I would recommend 3x3 tiles or smaller
I can supply you with tumbled travertine from Mexico which is very popular here in the Southwest Desert. E-mail me if you have an interest in the tile or any of the products we use on tumbled in the bathroom.