Hi there!
I voted "OTHER" because I think that it depends. I've recently introduced my daughter to the shotgun....she's 10'years old now and not a very big kid.
We'd been hitting the clay range with her .410 side-by-side and despite having put a tonne of work into getting the gun to fit her (it had an 11 inch LOP when we were finished) and the fact that she was hitting ok at close range, she was getting a bit frustrated. She was death-to-squirrels though and we've been out quite a bit to hunt them so she would have material for her aspiring hunting/cooking show on YouTube, and her success in this department was pretty good.
Here she is breaking her first clay with her .410
Then one evening we watched Terminator-2 together. She was fascinated by Sarah Connor's pump gun in the final scene of the movie and wanted to know if she could try mine (a 12 gauge 870). Frankly that idea was kinda scary for me but she was pretty persistent.
So the next day I went and looked at the Mossberg Youth Mini and the Remington 870 compact Junior. I chose the 870 compact junior based on my perception of how it would fit her with it's 12 inch LOP and the softness of the recoil pad, and I got it to the range to try myself side by side with her .410 to try and imagine what she'd feel. With standard 20ga shells my assessment was that it was going to beat the snot out of her, so I took it home and machined a 12 oz brass weight that I put in the stock. I also bought a couple boxes of Winchester featherlite 7/8oz 900fps target shells, and my perception was that the new combination kicked less than her .410.
She was thrilled when I showed her the new pump gun, and for our first range trip I made sure to bring my 870 along instead of my over/under so we could be pump gun buddies. Hasta-la-vista baby! At the range I let her load two so she can pump the gun which she loves, but when we're hunting I only feed her a single shell when she's all set up on the squirrel.
Here she is at the clay range with her new 20 gauge
Now 4 months later here's how she hunts squirrels
I'm getting a bit tired of picking a zillion #8 pellets out of her squirrels before we cook them, but I'm going to wait a bit before upgrading her to a more powerful load as we're simply having so much fun now and I'd hate to turn her off her gun.
The 18 inch barrel of the compact junior also turned out to be important...she's small enough that if she uses a 21 inch barrel (we tried the 20 gauge youth model too), the barrel is long enough that it stabs the ground when she holds it at low ready.
The last piece of advice I might offer is to set the new participant up for the highest degree of early success imaginable. When at a sporting clay range this means striking a deal with the course operator such that during times of low activity we can move into the course a bit outside the stand and position ourselves so the clays are hanging right in the sweet spot for her or shooting straight away with her standing right beside the trap. Only once she has built confidence in hitting these do we start to move back towards the stand or laterally along the trajectory of the clay. My daughter can now easily hit outgoers and incomers, and we're slowly introducing crossers. If all I had to work with was a skeet field, I'd start at station 7 on the low house, then slowly introduce the high house. After getting some success there, I'd move to station 1. I'd avoid the rest of the field like plague until we were getting good hits on the outside of the field.
Part of me thinks the .410 was a bit of a waste, as it was only about a year until she was into the 20 gauge and handling it like a champ. The other part of me is glad I went with the .410 as it was a cheap gun that I did not mind cutting down to the 11inch LOP required to make it fit ok and it got her feet wet and stirred her imagination.
Cheers, and I hope you have as much fun with your newbies as I'm having with my daughter!
Brobee