[Zeke]

If you hit the back side of the door and window casings first, then do the walls first. Also, while most tape does bleed, if you run a nylon comb over the sealing edge, it won't. When you caulk the trim to the wall, don't leave a big radius. Next day run a dull knife down the caulk line. It will leave a score mark that you can cut dead nuts to.

Of course there's always the tenement way to paint: paint it all Navajo white semi gloss. Walls, ceilings, cabinets, everything.