The recoil in my 7X57,
when firing factory 140 grain ammo is almost non-existent. It produces a muzzle velocity (MV) of about 2660 fps - about 200 fps faster than a 150 grain 30-30 load.
Factory 175 grain ammo has noticeable (but quite bearable) recoil, with a MV of about 2440 fps - about 200 fps faster than a 170 grain 30-30 load.
That said, you could say the 7X57 is a 30-30 shooting +P loads (if they made such a thing for 30-30).
If, however, you handload, you can boost the velocity of the 140 grain 7X57 to about 2,950 fps, nearly equal to factory .270 Win velocity. The recoil, in that case will also be very much like the .270. Too much, in all likelihood, for most kids.
Then, of course, you can handload it down to less than full velocity, to reduce the recoil, and/or substitute lighter bullet weights (I think 110 grains is the lowest you can go) to reduce recoil.
When it comes to availability of factory ammo, you won't find 7X57 on every shelf with the .243, .270, 7 Rem Mag, .308, 30-30 and 30-06.
But places like Academy, Gander Mountain, Bass Pro, and Cabela's will stock it. Winchester and Remington are the most common, but Federal and Hornady (including "Superformance" at 2,750 fps for 140 gr) loads can be found, too. A local gunshop orders the 175 gr load for me (a great hog stopper!).
Ammo prices are only a few dollars per box more than the .243, et. al., unlike the nearly double price asked for the WSM series, and/or the premium bullet loads.
The 7X57 has more than enough killing power for deer - really lays them down! But not for long distance (anything in excess of 300 yds).
Not a precision cartridge, but you can expect groups of about 1.5 inch @ 100 yds, or so, depending on your individual rifle.
