If you are looking to do this at a fairly low cost, I would look at the Stevens or the Marlin XL7. Both of these have tested very well, with groups running from 1-1.5" at 100 on average.
If you are going to go with the Stevens 200, I would look at it in .308. I have been shooting a fair amount of the Remington managed recoil in .308 and 30-06 and it has been very pleasant to shoot, along the lines of the .243 in recoil. The .243 may have those beat in energy out past 200, but if the shots are under 200, the managed recoil loads would work fine. This also allows her to use the full power loads in .308 or .30-06 if needed and she can handle the recoil.
As the Marlin XL7 is only offered in long action right now, I would look at the .270 win, which has done very well in this gun for about $275. Managed recoil loads can be had in the .270 win, which would be rather mild, while full power loads are not too bad.
If you want an H&R (which does not save you much over the two above), I would look at the 30-30 as well. The .243 has been hit or miss accuracy wise and since remington took over H&R there have been some hiccups with service.
Whatevery you choose, make sure it fits her before buying it, otherwise it won't be fun for her.