simple and cheap break off shotguns, to me henry has always been the affordable lever action .22 (ive had one since i was a kid) with that being said, i think henry could out compete the other brands who make single shot shotguns and with your name, it could be a mass produced gun like the lazer, bioto, olympic etc. also i recently heard that lazer went out of business so there is an opening in the market!
my gauge suggestions would be the smaller gauge guns, everyone wants a cheap first gun for their kid for christmas, 12 gauges would likely be too big, id recommend .410, 28 gauge and 20 gauge, in my local market (newfoundland) a basic single shot 410 will run $200 and up and they are hard to find, especially the backpacker models with short barrels, if you wanted add on cost items, you could produce them with longer barrels, colored stocks, fiberoptic rifle sights etc. thanks for reading!