I think I am a bit late to add to this conversation, but I wanted to add some information from personal experience with growing a P. caperata (I doubt the care of other species is much different).
They don't grow a vast root system like a number of houseplants, so potting in a larger pot is rarely necessary.
They enjoy bright, indirect sun, but I believe morning sun is okay (especially for the variegated varieties, if they don't receive enough light, they will lose their variegation over time). Mine does receive a little bit of midday sun from a South window, but during the summer, I wouldn't advise that at all (especially in my zone... I'm in zone 8). I read on another forum of a lady who grew hers in a West window year-round (but I believe she is from zone 5?). I know West would be too harsh for them in my zone.
With respects to watering, they don't like to "stay moist," but prefer to dry out a bit between waterings (not completely, but don't try to keep the soil moist at all times either.. somewhere in the middle if that makes sense).
I picked up a Peperomia the other day that was grown by Exotic Angel. I have had the hardest time finding the exact "species" online, as none of EA's plants match, haha. I think it's P. pecuniifolia (even then, I only found but a couple pictures online when I typed this in). Cute little plant.
If you're ever interested in looking at an adorable Peperomia, check out P. polybotrya (I believe that the species).