kits generally have stuff you don't want or need
this might be a time for a boresnake, generally I point out that a boresnake doesn't do anything to clean the moving parts of the gun, but a single shot break action shotgun doesn't need much cleaning other than the bore, now does it? You'll still want a basic patch pusher/puller and a brush for the initial sweep through the bore, but a snake might be the ticket for such a simple gun, coupled with an occasional clean/inspect of the action.
Some rod and a couple brushes, perhaps a selection of patch sizes and thicknesses and a brass jag in any bore size you use ... and some basic solvent/oil/grease ... and a spray-can of CLP ... and compressed air ... and an old toothbrush
that's pretty much all you'd need for basic rifle-shotgun/handgun maintenance, nothing you couldn't get at a well-stocked Wally World, except maybe the jags and anything beyond basic patches
the only KIT I've ever been glad I bought was one from Otis, where everything gets dragged through the barrel on a flexible cable ... the kits are expensive and I end up using mostly just the cable out of them, I even punch holes in my own patches most of the time