Controlling recoil for younger shooters may also involve a properly fitting rifle for their stature. Too long, or too short of a stock can make it more difficult to properly hold the rifle, and accentuate recoil. A good recoil pad is also important. There is no way around the fact that very light rifles kick more, it is a trade off.
Maybe they still sell the rifles with stock combinations, or if not they may have the different stocks available.
Am a strong proponent of hand loading, but do lot more shooting than hunting. However if you are only hunting with a commonly available caliber and find a load that suits, hand loading may actually more expensive.
Having had a daughter myself start out hunting at 6yrs old and then a nephew along behind her, then my oldest grandson wanting to shoot himself a pig at the ripe old age of 3, yep I can say I have had some time spent with the kiddo's and the issues which plague them.
What Zeke posted above there are a couple of VERY valid points. Trying to have a youngster or hell even an adult learn to shoot a rifle well with a stock that doesn't fit them is a REAL pain, literally sometimes. That was my biggest hill to overcome. All of these kids were and are still pretty light framed. Most everything I own has around a 13.5" LOP which is LONG for a kid. What I found for my daughter was an old Remington 760 in .243 which fit her far better than anything else we had or could afford at the time. The nephew also used it but he was a bunch bigger than my daughter in his early teens when he started but graduated to a .25-06 after getting the hang of things.
The grandson, well I tried everything I could to work around him getting behind the trigger, but he is a red toe headed kid and once he has his mind made up your not changing it. So I downloaded some rounds for my .308 with 125gr bullets and using my Ruger Compact, which was all he could manage, he practiced all spring and summer long. As we went along I would bump up the charge weight just a little, bout a half grain or so of H4895. When fall came and two weeks before his 4th birthday he DID in fact put his first hog on the ground and in the freezer. He hasn't let up since. He just turned 13 Thanksgiving day and put a 300+yd shot on a 10pt buck using my 25-06 AI.
All this said, like Zeke mentioned if your working your daughter into this, find something that fits her, forget the caliber be it a .243, 7-08, 30-30 even, fit or the ability to do so is what will matter. If she cannot get in behind it properly from the get go, even the best of reduced loads aren't going to make her feel any better about shooting it. Not to mention being able to get a full sight picture in the scope, or proper placement of the butt pad on her shoulder. With a good fitting stock even shooting a full blown .308 isn't bad as most make it out to be. Mine only weighs 6.5# sit sling, scope, and 5 rounds in it. The daughter, my grandson, and several friends all felt like it was far easier and more comfortable to shoot then they initially thought it would be. My grandson even was calling it "our" rifle for a while.
I put him together a nice Sako in .243 which he really likes and uses once in a while, but he is VERY partial to my .270 which I am putting a new stock on and will probably pass on over to him this spring.
For shooting I always started them out slow with only a couple of rounds in the centerfire followed by some through the .22. After a few weekends of this we moved on into nothing but the centerfire but still only increasing the number of shots from around 3 per session to 5 or 10 per day on the weekends. After a month or more of this we were up to shooting a full box each day of what ever we were going to use while hunting, and were shooting targets set up at range angles and ranges. I used the full sized archery deer targets and some 1/4" plywood to back them up with and some 3/8" rebar on each end to ty-wrap them to. This made it about as realistic as I could without actually putting them on critters.
The point of it all was to get them accustomed to getting the rifle up and in the ready position, not knowing which target I was going to call made it a challenge. Once I called out the number, they had to adjust, acquire, aim and fire on it all on their own. I made it clear from the start with them all, if they couldn't do it, they weren't going period. This said I DID help each of them get the rifle up and ready when the time came but up until that moment, they didn't know I would, but they had the confidence to do it themselves and not be second guessing what they needed to do next. Each drill they had to get on target, aim, fire, chamber another round, and put the rifle back on safety. Each step wsa practiced many times with an empty magazine as well as with live fire so they were fully accustomed to it.
All of them did excellent their first times out and have every since. So while your considering picking a caliber, and starting to handload, like Jimbob mentions you can quickly pay for your equipment while shooting practice rounds and learning the nuances of your new rifle and scope. Speaking of scopes, be sure to look at the Weaver and Bushnell extended eye relief models for that kiddo. It will help out a LOT not having to creep up on the scope some if the stock is still a touch long. Plus they keep the scope out in front so it doesn't get upside their head too.
