I also use Pedro’s Orange Peelz. If I’m doing a full cleaning, I will remove the chain and let it soak in it for a little while, dry and replace. If I’m just doing a quick cleaning, I’ll take a sprayer that attaches to the bottle and just give it a light spritz.
As for lube, I’ve used many brands, but found that White Lightning does pretty well. I also use Tri-Flow’s Superior Lube / Dry Lubricant. As previously mentioned Tri-Flow does wonders on pivots, break leavers, and derailleurs.