I use G-96 spray and wipe with microfiber cloth. I also have one of those microfiber cloths soaked in an oil that I keep in the gun case in teh event of rain. I use grease applied by hand or a small brush for lubricating the hinge points.
For well over 45 years I have used a soft shaving brush. Put a few drops of oil on it, and it will leave a very thin coating of oil on the exterior. This is the last step in cleaning and oiling before putting the gun(s) away. Works great on shotguns, rifles, pistols, etc.
The quest now would be to find a shaving brush ;-}
I have a 2yard long by 1 yard wide piece of gray flannel...I use pinking shears from the sewing kit to cut out a nicely edged 8"x 8" rag that I use Militec synthetic oil...also use Amsoil marine 4cycle with extra rust inhibiters..after the rag has the right amount of oil in it I put them in very small ziploc freezer bags then keep it with the gun in its case...very cheap and always handy
Bore patch lightly lubed with Clenzoil to apply a light coat on most areas. Artist's brush for harder to reach areas. I go light with everything unless I'm prepping the gun for longer term storage and even then I don't overdo it here in West Texas - dry climate.
I'm very anal about this subject. (Yeah, right) I buy my ultra soft yellow micro fiber clothes from Costco in a bulk pack. You know, the very expensive $4.00 per 24 pack ones, not the $2.50 per 24 pack of those cheap terry cloth types. I very, very, carefully spray a cloth with about 3-4 squirts of Scott's Liquid Gold Furniture Polish and slowly, but, gently, wipe and massage the gun down with this set-up.... lol. A drop of the cheapest 30W motor oil I can buy on the hinge pins, barrel ears, and the forend surfaces, and a shot or two of Break Free in the Precision Triggers and I'm good to go. Has worked fine for over 30 years.. Dan Thome (Trap2)
A couple years ago there was a similar post about how to best oil/clean the inside of a shotgun barrel. Some joker replied with something like, "I use a pair of my wife's panties and pull them through the barrel with a come-along." That might still be the funniest thing I ever read on TS.com
Using a big cloth like a mitt or piece of t-shirt doesn't get oil into places like under the rib or between the barrels of an O/U. About the only gun I ever wiped down with a big cloth were plain-barrel Mossbergs. You could reach anywhere on those guns with a rag. I prefer to wipe my O/Us with a patch that gets where I need it to go.