My wife is not much bigger than you and her favorite rifle for larger game such as elk is a Remington 700 Stainless Mountain Rifle chambered in 270 Winchester. I put a shortened stock on her rifle and a Leupold 3.5 x10 scope on top. It is light weight, has manageable recoil, is very effective on game, and fits her. She shoots it well and has taken a few elk cleanly with it.

A common cartridge such as the 270 makes finding ammunition very easy nearly anywhere on earth, and it is often priced better than ammunition for less common cartridges. Something similar would be a good starting point for your search for the perfect rifle for you.