I think too many people underestimate the impact (no pun intended) that recoil has our shooting habits as we develop and our ultimate shooting ability. I've seen a lot of 200 pound men with visible flinching even with a non magnum 30 cal. I've got a cousin that can't hit the broad side of a barn due to a terrible flinch he won't admit he has -- and he's never hunted with anything bigger than a 308. Personally, I don't care for guns that kick hard and I'm not ashamed to admit it. I'm sure my daughter would just quit shooting if she found it unpleasant. My son is so keen that when he's old enough I expect he'd tough it out, but maybe develop a nasty flinch that's really hard to get rid of.
Keep it painless, keep it fun. It takes a long time to build really good shooting habits, but it takes a heck of a lot longer to unlearn bad habits.
A 243 is an obvious choice, but Remington Managed Recoil loads in 270 or 308 would achieve the same thing.
I think a lever action is a terrible choice for a new shooter - particularly one with a tubular magazine since you have to jack the shells through the action to unload the rifle. A new hunter has far too much going on in their head - don't make it any harder than it needs to be.
Good luck.