C.P.
I do the same: Pour in toilet, rinse and slosh with a little water, pour in toilet. I've discovered that leaving a little bit of water in the bowl helps keep the smell down (just like in the toilet) and it helps keep the poop from "sticking" to the bottom--gross! About once a week I wipe down the potty with bleach wipes or other multi-surface cleaner and then rinse in the tub.
As for wiping, I do let my girl wipe with a small piece of toilet paper, but then I wipe her with fresh t.p. (and a baby wipe if there are any drips or poop). At her daycare, they just let the kids wipe themselves, but I do try to show her how to be a little more thorough.
Good Luck! It's great once you get to the point where you don't need diapers/pull ups anymore!