Stone is less forgiving than ceramic tile. You want to take virtually all flexing out of the floor. You can do this any number of ways. Adding 7/8 inch fir plywood, or 1/2 inch hardi glued down with a layer of thinset and screws will do the trick. Dens shield is great for walls, but not for floors. GreenE board (a white cement board)is also good and easier to work with than hardi.
If you have access to the joists underneath install some bridging or blocking every couple of feet.
Use the span calculator on this site to make sure your floor is ok for stone L720 deflection.
White marble needs white thinset, as it it slightly translucent and you can end up seeing ghosted trowel lines. Otherwise marble is easy to cut and shape. I like to take out all the tiles I have and arrange them in a pleasing pattern, matching up the grain as best as possible. keep grout lines minimal and really take care to eliminate lippage.
Green marble needs 100% epoxy solids thinset or it will warp.