I stack them on their sides on top of something flat that doesn't change moisture or temperature. I usually set mine on top of a platform I built in the basement out of a piece of 3/4" OSB and some 2x4s. I stack the first one outside up, second one outside down, third one outside up, fourth one outside down. This keeps the pretty side (if you had white letters it'd matter more) from meeting the ugly side which probably has grime, grease, and road tar on it. It also makes it so the ugly side is face up on the top so if you're like me and use piles of tires for workbenches you won't leave anything on the pretty side.
I wouldn't bother treating them with anything if they're going to be inside. Just don't let a hot air duct blow on them. I clean my tires with Lysol Basin, Tub, and Tile cleaner. I then let them dry and apply Armor All's "Flashblack" on them. I wait a couple minutes to let it soak in and then hose it off before it "dries". I like the "new tire" look but I don't like the greasey slime look. By hosing it off before it dries you can avoid the slimey look and feel. Plus, anyone that has used the "tire wet" junk knows that if you go down anything remotely dusty your tires turn brown if they have the goo on them.