Congrats on showing your daughter the joys of hunting. I just wished more parents would do what you are doing.
I too recommend getting here the best in the ear electronic hearing protection you can afford her. There is nothing worse than seeing the effects of our sport on our children hearing test.Many folks cheat at this and think that 1 shot or 2 in the field won't hurt because they have done it before,but they are dead wrong.My hearing is permanently damaged because of this,and I pray you take these words to heart and spare no expense at protecting her hearing.
Caliber choices for her is open to a-lot more than just rimmed cartridges,since she has been successful with her other guns.Since you reload,you have your choice of all of the calibers available to you.Each have their own merits and fans as you can tell. Since your suggesting a 200 yard max shot,I can assume you already know your area and are making plans accordingly.If not,then some serious planning and scouting is in order.
Personal choices of mine for anyone that can handle the recoil of a 12ga.auto even in the rush of excitement are the 25-06 and the 270,with the 280 not far behind. I've had more fun and luck with these 3 in the Handi rifle over all others,save for my custom 338-06 A-Square W.York built for me.
Since you are a re loader,you already have at your disposal the reloading data for each and if you don't there are plenty of sources available here for what has usually been the best with both factory loads and reloads.Trying several of each is usually the best way to find out what works best for both the shooter and rifle,and you will need to dedicate that time to ensure her that it does.I have had great success using both factory and hand loads from my Handi's over the years and do hope your daughter shares the same luck as I have.
I might also suggest several dry runs during your scouting adventures,with her carrying her rifle (which ever it may be ) so that she builds up some extra strength and learns how to make it work for her. It will give you extra time to work out some of the little kinks that always seem to pop up on her opening day.
Make the rifle fit her in her hunting cloths.Nothing spells discomfort like a ill fitting rifle or shotgun. Get a shell holder for the butt stock and put some soft foam under it to take all of the face slap out of shooting it and to raise it so that she has a perfect clear and centered field of view thru her scope or even open sights if using them.Having a soft pad to snug her face into instead of a cold hard stock promotes the proper cheek weld and reduces flinching. Have...or install one yourself..a good recoil pad,at the lenght she needs for her hunting cloths.Remember,your fitting her,not yourself,and thinking she will grow into a too long of stock only makes things worse,not better. A few extra dollars ensuring that the rifle or shotgun fits the young person now, will net you and them a huge return on satisfaction and success,by removing the fear of it hurting them when pulling the trigger.
Good Luck
Mac