I clean mine (any/all of them) after I shoot them. Whether it's 15 shots or a couple hundred (most I ever shot in a day as a civilian).
I've used lead or plated bullets. My handguns/rifles don't show a difference in which is harder to clean and some of my guns really "like" the lead bullets. "Like" means they are both reliable and accurate, so why pay more for ammo that won't shoot any smaller groups?
I have 3 or 4 .22 rim fires that are 80 to 100 years old. The barrels look new - because they were cleaned and a lightly oiled patch run through the barrels after they were clean. You don't know, when you put it away at the end of the day, whether you'll shoot it tomorrow, or maybe not for months (or years, for some of mine - but I don't depend on them to feed the family the way my grandpa and great grandpa did).
I don't know what they used for powder solvent or lube oil that far back but I know when I was a kid it was Hoppes' #9 to clean and 3n1 oil for the lube.
Patches were easy to come by (any old worn out piece of cotton clothing could be cut into patches - something I do to this day, I haven't bought a patch for the bore or to use an oily cloth/wipedown rag for a long, long time) but I don't know about brushes. Brushes have a limited lifetime due to accumulated wear and the way you use them. Patches get used once and go in the garbage (or the stove back in those days - if it burned it made heat and heat kept you warm in the winter and cooked your food all year).
Regular cleaning helps keep stuff (crud) from builiding up in the chamber/bore/bolt face/extractor, etc. You may not be looking for advice on a "super cleaner" if you keep it cleaned/lubed regularly vs. letting it build up.
Some .22's can be damaged by dry firing, so don't dry fire unless is says, somewhere in the owners manual, that dry firing is okay - or if you buy/use snap caps (be aware snap caps wear out and need to be replaced at some point.) What happens, in dry firing, is with no round in the chamber the tip of the firing pin strikes the corner of the chamber where the cartridge rim would normally be. That can damage the firing pin or even the chamber. I used to know a guy who was into dry firing his Ruger Mk1. It got to the point it wouldn't completely chamber a shell and he finally looked at it good (didn't clean it much) and found the firing pin had dinged up the chamber edge there enough that a round wouldn't full chamber. He had to send it back to Ruger to get it fixed. On the other hand, the Ruger manual for the 10/22 specifically says dry firing is okay (or used to) due to the design of the bolt and firing pin. Read you owner's manual.
Good luck, be safe and have fun. An afternoon of .22 shooting with friends can make life long memories.