My usual process is to clear it first (of course), before I field strip it by removing the slide, spring, barrel, and grips. I run a wet brush with solvent through the bore first, then wipe everything down with a patch moistened with MPro7 cleaner (the least voliatile cleaner I know about that still works well), before working on the heavy fouling with a brush. I then dry with a towel, oil with FP-10 or BreakFree CLP, then go to work on brushing the barrel (now that the solvent has had some time to work on it), before running patches through it and finishing with an oiled patch.
At the end, I usually wipe down the surfaces that recieve the most fouling with an oiled patch to leave a slight film of oil, especially the breechface, the feeding ramp area, slide rails, and the inside of the slide. I find this makes cleaning easier next time. Remember to take the opportunity to clean the magazines if neccessary.
If you get the Inox, cleaning will probably be a bit easier than with the bruniton; at least, you'll be able to see what you're cleaning much better with the stainless.
This is probably overkill, and you can probably get away with just cleaning the bore between every 3 or 4 range trips, but I like to keep my guns as clean as possible.
Also, it doesn't hurt to know how to detail strip your gun when you get really paranoid. :lol: