When my girls started hunting, I found a used Ruger M77 in a 6mm Rem. with a bull barrel. I then bought an extra stock off of eBay and took 4" off of it. Great fun, most accurate gun I have ever owned. Shoots quarter-sized three shot groups at 100 yards using Remington Core-locks. The bull barrel really takes the kick out of it. My youngest took her first deer with it when she was 10 and only weigh 86 lbs. Her first deer was a doe at 225 yds. She is 17 now, and I had to put the long stock back on it this year. She finally grew into it.
If you can get a gun with a bull barrel, I would highly recommend it. It will really soften the kick. I really like the 6mm but ammo for it is limited and can be hard to find sometimes. The 6mm's ballistics are very similar to the .243 however. My daughters have never had a problem killing deer or hogs with it.
The other thing I would highly recommend is to be sure you spend plenty of time at the range with them before you let them shoot at a live animal. Let them get to where they are fairly accurate with the gun before letting them shoot at a live animal. It can be very traumatic for a kid to wound their first deer and have to track it and finish it off, etc. When possible, We usually go ahead and put a second bullet in a downed deer before we ever get out of the blind. It can save you a lot of drama especially if you are hunting with girls.