Should I grout the walls or floor first?
I can not think of a reason that it matters. 

I would do the walls first, i would protect the floor with some heavy duty plastic sheeting taped down at the edges. 

Wait a day and Then do the floor, use painter tape around the base of the walls. 

After the grout has cure for a day then you can pull the tape off the walls and caulk the joint where the floor meets the walls with 100% silicone, mold and mildew resistant caulk.