I'd start with a top-quality rifle in .22LR as a hand-me-down, and then see what happens in terms of interest, etc.

AD

I could ramble on about this one.
Since we are talking starter guns that will always be useful.
A .22...ruger 10/22 would be ok,but for a little more you could have a Rem 541-T.

A .308 win or rem...either would be fine. One of each would be better. 7MM-08 would be ok too. Anything else in the hands of a youngster I would consider a crippler.
There are many that started out with .243's, or for birds, a .410. I think these are for experts. A .20 gauge would be better in my opinion. Maybe a 870... Thought I'd through in a shotgun.
Your choice in hand guns will work. I'm not a glock fan,but they are good guns. I like a s&w mod 41 and kimber .45. There are so many good choices. If you like revolvers a s&w mod 617 and 629.
I'm don't know the answer to the short mag thing,but I think all the others work and I think many will stick with them. I have a few m-700's in my safe in 7mm rem mag.and they work just fine. I'll buy a short mag... probably in .300. or .338.
You did't say if money is no object...

My hand me downs will be all my guns. By the time my Boys get them I won't worry about how they divvey them up. As for starting them off, I made sure that they each have a 22lr, a 30-06, and a 12 ga. With those they can hunt anything except dangerous game and if they're going to do that I'll go with them and bring the guns.

My grandfather gave me his Win mdl 92 in 25-20 Win. I killed my first deer a little 3x3 blacktail with it. I think what matters is how much the gun ment to the original owner. I redid my will a few years ago and rethought about who I was giving what to. I like hunting rifles, while others like combat pistols or varmint rifles or shotguns. I wouldn't worry about the caliber if they are into hunting and shooting. If they are a once a year hunter or shooter maybe 270, or 3006 is the best choice.

I have 1 hand me down and one sprta hand me down. The first is a pre-64 Model 70 Westerner in .264 Win mag. I love this gun and took it and shot 1 cow elk with it. After that it was retaired for safe keeping. The second was a gift from my parents and grandparents for my first rifle. It was a 25-06 Browning Gold Medalion Sporter. My grandpa had used it for a few years then my parents bought it for me at a cheap price as part of the gift from my Grandpa. The 25-06 is a perfect all-around choice for a beginner.

Something to think about, and this why my Dad chose the 25-06 for me is shooting fundementals. He wanted to instill in me that bullet placement means everything in shooting. With the 25 I had to shoot for the heart/lungs area of big game. In doing so I dropped 6 Muley's, 5 elk including 2 6x6 bulls, and 1 B&C Bull Moose. All were 1 shot kills.

Now I carry a 7STW(obviously) as my all arounder for all North American game with a .243 as a back up that will be handed down to my now 4 year old daughter.

I amnot a fan of any of these carts. but they will be around for along while & get the job done;.308, .30-06 & .270.
Any handgun in .22lr is a good bet. Again, not my favorite, but practical. A good 4" .357 is the next step up. Semi-autos are for people who shoot often, if your kids don't stay w/ the rev.

Nebraska,

Check out the latest issue of Rifle magazine -- Ross Seyfried has an article on how to adapt a youngster to a .30-06 without flinching, and John Barsness has an excellent piece on "recoilless deer rifles" (light kickers from .250 Savage through 6.5x55 up to .300 Savage and .308 Win.).