My sugestions for your sons
I have a 15 year old that has no problem with the recoil of his 30-06 that he chose/stole from me. It might be more of a problem with the 11 year old handling the recoil of any Deer class cartridge. For starting I had both of my boys shooting 22 rifles. I think that this is very important that they learn the basics of rifle shooting without the recoil or blast of a Deer class cartridge. If you are ready to buy something for them I would recommend a standard rifle cartridge. A bolt action modern hunting rifle in either .308, .270, or 30-06 will last them a lifetime. Marlin makes an entry bolt action the xl7 that can be found onsale for under 300 dollars. Something used could also be found for your boys at a gunshow, but make sure you have a gunsmith checkover the used firearms before you shoot them.
Karl
I have a 15 year old that has no problem with the recoil of his 30-06 that he chose/stole from me. It might be more of a problem with the 11 year old handling the recoil of any Deer class cartridge. For starting I had both of my boys shooting 22 rifles. I think that this is very important that they learn the basics of rifle shooting without the recoil or blast of a Deer class cartridge. If you are ready to buy something for them I would recommend a standard rifle cartridge. A bolt action modern hunting rifle in either .308, .270, or 30-06 will last them a lifetime. Marlin makes an entry bolt action the xl7 that can be found onsale for under 300 dollars. Something used could also be found for your boys at a gunshow, but make sure you have a gunsmith checkover the used firearms before you shoot them.
Karl