Well I am not concerned about filling tags nearly as much as getting the kids out in the woods and off the couch. I started my daughter out when she was barely 6 shooting a 22 pump and shortly afterwords moved her up to a pump .243 Rem. She hardly weighed in at 60# about this time, and the rifle was a bit bulky but she had the desire to work through it. Three years later a buck finially cooperated, and presented her with a shot, she used my 25-06 to make a one shot kill at 185yds. Funny thing is the .243 was there she just didn't want to use it.
The grandson told me early last year that he wanted to shoot his own boar hog. He was 4 1/2 at the time, and serious as a heart attack about it. I started working on something for him to use and ended up starting him out on paper with a M1 Carbine as I had a limited choice onhand of short stocked rifles. While we were there I also let him shoot 3 reduced loads from my Ruger Compact in .308 which he didn't group nearly as good as the M1 which left a lot to be desired. However after several times with both he decided that he really liked the .308 and was doing really good with it. Opening weekend of last deer season he dropped his first boar hog using the .308 and has more or less laid claim to it.
This year he has gone through almost 2# of powder shooting 38gr loads with 125gr bullets. The velocity is only about 2200 fps but it still works great out to the 50 -75yd limit I keep him in, and he can easily group them around 1" at 100yds. So far he has taken a yote a couple weeks back at just over 150 yds with it, then missed a small buck at 75. I have a hard time finding fault as he was definately excited about it and so was I, and I can honestly say it happens to even the most seasoned hunters.
Before the season started I put up multiple full sized targets at various ranges in the area we hunt, and from the same rest he used for hunting, had him shoot at each one as I called them out so he would get used to the varied distances and different angles the deer were looking. At first it was all different than the one target which had an orange spot to shot at, but after the first round at each and some explaining of where and why to shoot them, he put it together and was making kill shots from then on out.
I am a firm believer in anyone who hunts being able to shoot the rifle they intend to hunt with no matter the caliber. IF they cannot shoot at least a 2" group they haven't shot enough in my opinion. This is just the way I was raised and it has seemed to prove itself correct through the years. The less variables there are in a load and accuracy of the shooter, the more effective they are in the field under moat any circumstances. As for the boy and his miss, we only had a few seconds to get him set up and ready for the shot before the buck would have been out of sight. Add this to his and my excitement and well we blew it. As mentioned, it happens, and it was a clean miss as the same deer was within 15yds of the daughter the very next weekend with no signs of a hit anywhere.
As to the best caliber to start out with, there are several considerations which to look at. First is the physical size of the shooter, lenght of pull, game intended to be taken. Once these are satisfied then there really isn't any reason that any centerfire from a .243 up could not be a good choice in today's world of recoil reducing aids. There are slim pads which can be worn over or under coats and shirts, muzzle brakes even though noisy, reduce felt recoil by about half or more, various calibers which can now be had in factory reduced loads not to mention handloaded, as well as a whole list of calibers which if shot in a properly fitted rifle do not produce a lot of felt recoil. I believe that if more folks would spend a little time getting a rifle to fit either by buying it that way, or having the stock cut or lengthened they would be much better off. It's hard to find a rifle which will fit a youth properly without having it a bit long generally, but those who look into it will find they will shoot them much better and the recoil of even full loads in the mid sized cases will not be too offensive. As to the .223 which was mentioned, with today's bullets and keeping the range down to 50 or 75yds this caliber can be very effective on deer sized game with proper shot placement. There are a couple of factory loads which do a very out of proportion job considering the size of the bullets. Would I choose it over something else, no, but I have used my Contender pistol in .223 to dispatch some decent sized hogs out to 100yds using bullets which were not designed for such an animal. However with the proper shot they hit the dirt with authority. Here again the key is shot placement and not overall knock down power. This same round using a properly designed bullet is very capable of dropping deer sized game when they are hit properly, which brings us back to range time.
Me I spent about an hour and a half at the range before opening weekend shooting two different rifles. Does this make me a weekend hunter, due to the time spent, or does the previous 18 - 20 weekends of firing multiple rounds from various rifles out to 500yds get to be added into this time? Sometimes I think we all see someone shooting only a handfull of bullets, even through a new rifle and figure them to be one weekend hunters. This might be the case a lot of times but not always. As to a single shot rifle, most folks I know who are great hunters and have years of experience rarely get the time for a second shot if the game runs on the first. Most of the hunting is close quarters in the woods and the first shot must generally count. Even in some areas with feed pens set up, once a deer is hit it generally leaves the area, and hitting it on the run would not be a reasonable thing to expect a youth or new hunter to accomplish.
Sorry for the long post but just some things I saw in this that were either based on personal opinion or lack of actual facts. Even those kids or wives who are getting new rifles a week before the season opens, might have been shooting for months before, and even using what some consider a marginal caliber might be better hunters and shooters than those using something a whole lot bigger.