Your trim and doors most likely have a lacquer finish on them now. You can paint previously stained and lacquered doors providing you scuff sand and prime them with a suitable primer. We typically use a Shellac primer from Zinnser.
Spraying is the best method for applying the primer and finish coat. The finish coat can be high quality water base enamel or Alkyd Modified enamel. The Alkyd Modified Enamel will provide better adhesion.