I use Hornady OneShot for cleaning of firing pin and channel, chamber and bore. I use... I think it's KlenzOil, a moderate viscosity oil for barrel, slide, and most other stuff. I use RemOil for the sear cage and areas where I want the oil to run into (since RemOil in my experience is pretty runny, at least more than KlenzOil).
I try to stay away from grease. As already mentioned, it attracts crap more than oil. It's also a pain to clean off. When oil dries, it's gone and you need to relube. When grease dries, the oil on the grease is gone, but all the soap crap is left over. I'd rather lube more frequently with just oil than spend time cleaning dried grease off.