I would think a 157-160 would be perfect. Do you need a 160-no probably not, but since you are still a newb you may find a slightly larger board better for stability.
Also most rental shops allow you to swap boards when you are renting. I would start with an all-mountain camber, and maybe try to sneak in a few days with a rocker and/or a hybrid. This way if you do start to buy your own gear you have an idea which board you like the feel of the most. When I went to Zermatt for 2 weeks I tried a couple different board, just because I could.
Also the one item I would consider pulling the trigger on is boots. I'm not a big fan of boot rentals.