A Browning BPS is not a more reliable gun than an 870, sorry. The Brownings that cost more are due to nicer wood and nicer bluing. Plus, there are other reasons why a shotgun (or any other product for that matter) can be on backorder other than being the most commonly-purchased shotgun.
As for the youth shotgun--There is something about the firearms industry today, few companies have a clue how to make a youth shotgun... My son is 8 years old and I got him a Rem 870 Express 20 ga YOUTH with 21" barrel-- but it had a 13" LOP, so I had to have it cut down to 12" to fit him. It fits him perfectly now, and the 21" barrel is the perfect "ratio" for his LOP (perfect balance, well--for a pump anyway).
For the future, I have been looking for an "intermediate size" (halfway between his starter gun 12"LOP/21"bbl and adult sized 14"LOP/28" barrel)-- 13" LOP with about a 23-24" barrel, but The Remingtons that have the "adjustable length of pull" system have a stupid-short barrel length (18.5 inches). Talking about a worthless shotgun once the kid grows into the 13- and 14-inch LOP. Too short for anything other than home defense.
I am rambling a little, but my point is that a shotgun has to FIT CORRECTLY(length of pull) and BALANCE (barrel length that is not too short that would make it "whippy" like Remington's brain-fart 18"-- AND ALSO not 26-28" LONG with a short length of pull that makes it hard to swing and hard to hold up).
If anyone has any suggestions on a good shotgun (auto) with 13-13.25" LOP and a 23-24" barrel, they are welcome. The one I think I did find while browsing online was a Browning SILVER MICRO MIDAS, but to the point of my first comment above, it is relatively expensive ($1179 MSRP = probably $900-1000 sticker). However, if it balances well, and doesn't require gunsmithing to make it fit right, why not? That may be what I get him after all (and my younger son who will eventually shoot both).