I'm not a big fan of auto loaders but this is a time when they fit the bill.
My wife who is also recoil sensitive along with my sister both shoot Rem 7400 one in 270 win and the other in 280 rem, both have good recoil pads.Both of these guns have harvested elk under 200 yds and have worked well on deer.For a novice rifle hunter these would be a good choice for deer and the every once in a while elk.
The 7400 is not the greatest auto loader,the BAR or the Beneli R1 are top of the choice.
The recoil on both the 280 and 270 is so minimal the target bearly leaves the scope,with these rifles.
BBJ