Others with better qualifications may have better ideas, but I'll try: For handguns that shoot cast or swaged lead, I use a Lewis Lead remover - saves lots of time and solvent. For all handguns I also use, Wipe Away cloths, Hoppes #9 and Shooter's Choice solvent, Bronze and/or Nylon brushes - bulk packs from Brownells or Midway, and Kleenbore or other brand of steel one piece cleaning rods. I use nylon or brass jag tips. For lube I use Rem Oil, and sometimes a dab of RIG Stainless lube. I use rubber gloves when using Shooter's choice and try to keep my area well ventilated. Sometimes I use one of the spray gun scrubber products by Lyman or Birshwood Casey to blow out the works on semi autos when I don't want to disassembe (Ruger mk2)- USE GOOD ventillation or go outside. I buy bulk patches from Brownells and Midway - but since I use so many patches, I make a lot out of any clean old woven cotton fabric available. I tear it in 2 in wide strips fold the strips into 2 inch squares -rolling as I go then cut with scissors to size - do it while watching TV so I maintain a good supply. And I use a bore light. I NEVER use Stainless Steel brushes and try to avoid even bronze brushes on my 22s.
I try to clean ASAP after firing to keep the gunk from gettng hard. I carry an aluminum 3 pc rod, jags, and patches in my range box and usually run a few Hoppes 9 soaked patches at the range while the gun is warm - makes cleaning a little easier when I get home. Some times squiret with gun scrubber at this time too.
At home I run a few solvent patches thru then look down the bore. If I see lead, or if I know I have lead build up I run 1 or 2 Lewis lead remover patches through to muck it out - works good. Follow with solvent, until clean - maybe run a Wipe Away patch thru to get the last lead out. Then more solvent and finally a light coat of Rem oil. I may run Lewis patches through the cylinders of a leaded revolver for clean up then same as bore. Wipe off outer surfaces with a solvent patch where there is carbon residue then dry off and a light coat of Rem oil.
NOTE: If you plan to use the gun in REAL cold weather say less than 15 degrees F, clean out the firing and advancement mechanism with gun scrubber and leave dry - no oil or just a teeny tiny amount of cold weather oil so the it doesn't get hard and gum up the works. This is where the Rem oil is pretty good- it doesn't tend to get stiff like some oils. I think Shooters Choice makes an oil that is supposed to work to extreme cold (-40 or 50) but I've never tried it.
Well if you haven't fallen asleep yet that's how I do it. Good luck.