I've shot ALL kinds of stuff through my P226 in the last 18 1/2 years. Lead round nosed rounds for steel plate shoots (jacketed ammo fragments and sometimes comes back toward the shooter) to FMJ and everything in between. Not had one problem feeding, firing or ejecting any of it.
Hoppes #9 or CLP will do fine. I sometimes use Gunscrubber on the barrel but otherwise I usually go with parts in a ziploc and spray down with WD40 to soak for about 15 minutes or so. Bronze then Nylon bore brushes with some CLP then jag and patch. Repeat until no carbon shows up on the patches then light coat of RemOil or similar. Same treatment with mags except I don't use the bronze brush and add a few strokes with an old toothbrush.
Exterior, just go with an old t-shirt and RemOil or similar and give it a good rubdown. Toothbrush where needed (muzzle end due to muzzleflash discharge) and pipe cleaners for the tighter spots around the breech block.
Update after your range trip.