If you can get close enough for a shotgun to be useful, the #1 and #2 steel shot should be fine. I would probably save my money, though, and use lead.
It's very rare that I can get close enough for a shotgun kill on a Jack, anyway. We are in different parts of the country, though.
With plans to eat them, my preference would be somewhere between .22 LR and .22 WMR (including .223 Rem with FMJs), for rifles; and .22 LR to 9mm Luger, for handguns.
"Such is the strange way that man works -- first he virtually destroys a species and then does everything in his power to restore it."