How do I install Travertine?

I am about to install travertine in my kitchen and dining area. They are 18" X 18" tiles. Currently there is a sheet of 40 year old vinyl on the floor on top of 3/4 inch particle board underlayment, on top of 3/4 inch plywood flooring. If I use HardiBacker and screw it down is that sufficient or do I need to use glue (thinset) under the backer board too?

Secondly, I was told several different suggestions on grout lines. I have been told to butt them up against each other (these tiles are squared off), i've been told go wide 1/4", go thin 1/8, and one guy said to go 3/16" so that the line stays level with the top of the tile and looks seemless.

I was told to seal the tiles before grouting.

Anyone care to correct me on this info? Thanks
Brian
Billings, Montana