I use alcohol too. Usually a shot-glass full of single malt to sip while I get to cleaning my slide.
For that, I use a method very similar to Christian's, except I use a 1/4" wooden dowel with a nice rounded tip on it instead of the metal rod. I also use 'J'-cloths instead of the cheese cloth. Very similar fabric and they cost me nothing. My wife buys them for cleaning purposes.
But I like the medical gauze idea. I usually do a full cleaning once a month or more frequently if the slide gets sluggish. I do an inner slide wipe down before each lubrication.
For lubricant, I have just about everything (coldcream, SuperSlick (old and new), Trombotine, SoM, SoM Comfort) and I switch back and forth with them from time to time between cleanings. They all work great, but I have used something better (more on that later). I have never had a problem with any build-up of any kind.
As for the best lubricant ever? Well, back in school I used to use a Johnson product called Clean 'n' Shine on the advice of our band director to clean our instruments. I once tried it on the slide, and wow! Insanely good! A tiny spritz would last for about 20 hours of playing (about a week or so back then). Although a tiny amount was all you needed, it was almost impossible to put too much on. Unfortunately Johnson stopped making it back in the early '90s. So sad.