Call me OCD, but same here. I may just run a bore snake through the barrel if I only shot a dozen rounds or so, but if it has been a while since I cleaned it I'll do a full field strip, clean, and re-lube regardless of round count since lube does dry out and can attract lint and dirt.
Concerning how to clean it, you'll get as many answers as there are readers of this forum. I field strip it, spray Hoppe's No. 9 down the barrel, over the breech face, down the mag well, and over the slide. I use a nylon bore brush to clean the bore and a toothbrush to scrub everything else. Sometimes I blast out blind areas with Gun Scrubber. Wipe dry with a rag and dry the bore with clean patches or a bore snake. A drop of gun oil on the firing pin and dabs of grease on the slide channels, where the barrel locks up with the slide at both ends, and the barrel lug where the pin and recoil spring contact it. Be sparing with your lube, you just need a film. Reassemble, cycle the slide several times to be sure everything works smoothly, and wipe everything down with an oiled gun rag then a clean rag. Hasn't failed me yet.