Okay, woods hunting. That means that a rifle set up for long range isn't necessary. Light and handy works just fine, with such examples as the Win 94 and the Marlin 336. Or, depending on a person's size, "youth" rifles; and then such as the Remington Model 7.
Generally, scopes are a big help for first and last light of the day. Mid-day, iron sights are fine. Me, I like scopes largely because of my eyesight: Old age and tri-focals.
Again, generally, bolt-action rifles are easiest for a novice to learn to shoot both accurately and safely. This last is, to me, a really important part when it's somebody new to shooting and hunting.
Suggestion: Go to a gunshow and/or to a major gun store. Feel and fondle and check for fit.
Cartridge? Not critical. I'd prefer the .243 on the small end, and for the hunting situation as described, no more than a .308.
2¢ worth...