Cleaning kits are pretty much the same. A handle, rods, brushes, and patch holder. I don't shoot my single shot shotgun hardly at all so keep it oiled once or twice per year. If I had a shotgun I'd still use the rod/brush thing, but would consider a bore snake.
I use a bore snake on the ARs and am completely happy with it. I run a brush down it the old fashioned way every now and then.
Pistols get the rod/brush treatment.
Some guys clean every thousand rounds. I'm not one of them. I clean and oil after I shoot since a body never really knows when he'll get them back out. Life being what it is, the best plans of mince and men, etc.
It sounds like you could get away with simply cleaning and oiling after each range trip, and revisit/reoil ever 6-12 months if not being fired.
IMO, anyway.