When its hot and humid, I use a flannel cotton cleaning patch, dampened a bit with spit, to clean the goo out of the barrel. I then use another similar patch, DRY, to dry the barrel thoroughly before I put in the next charge.
In the Fall and Winter, when the air temp is colder, and the relative humidity much dryer, I use just a damp patch to remove the residue, which tends to cake if you don't get it out quickly( the reason for the spit, or other lube). When its below freezing, i switch to useing alcohol on the patch to remove the residue. It evaporates quickly, and I don't need a second drying patch.
Because temperature and humidity can change over the course of a day, I have NO RULE OF THUMB regarding drying and cleaning the barrel. I examine every patch when I take it out of the gun, and off the jag. The amount and sliminess of the goo( or lack thereof) tells me what I need to do to keep the gun firing. It took a long time for me to learn this lesson, because, like you, and every other shooter I have met, I wanted ONE RULE to memorize and use all the time.
If you live is some parts of this country where its dry all the time, you can possibly have ONE WAY of cleaning your gun that works all year round. It would have to be at an elevation of at least 5,000 feet, and probably in the arid Western Plateau of the American West, West of the Rockies, and East of the Sierras.