I purchased a Howa youth rifle in .243 for my 23 year old daughter last year. She loves the gun (not expensive either). It was her first year hunting and only shot rimfire or pellets previously.

Stock fit will be important as will stock design and the weight of the rifle also. Auto loaders are nice to shoot but the added weight is difficult to hold up for some. I had my daughter just walk through the woods with me holding a few different rifles that I owned. After that I had a better guess as to what she would like.

There is a wide range of good "soft" kicking cartridges available as mentioned above. I will only add the .257 Roberts to the list if you handload. Availability of ammo may be a concern. I would stay away from the 30.06, .280, .270, 25.06 and all magnums unless recoil is of no concern. Most likely it is! Go with "soft" and work on accuracy.