The problem with 1100's is they are relatively heavy compared to older designs (the barrels are thicker) and nice ones run 400 bucks and up in 20 ga. Their advantage besides recoil is that parts are common and cheap.
Otherwise wait for one of these Marlin 31's or 44's to show up on Gunbroker in the $200 range. Nice, light little 20 gauges. 5 1/2 lbs. I agree that getting the kid's stance correct largely negates recoil.
http://gunbroker.com/Auction/ViewItem.asp?Item=143146727
http://gunbroker.com/Auction/ViewItem.asp?Item=142870689I can't find the address, but there's an outfit in PA that loads low-pressure shotgun shells designed for damascus guns that are real gentle to shoot. lhttp://www.classicusc.com/RST_Shotshells_s/139.htmat of them is quite reasonable, too.
Here they are:
