Just to make sure everything is clarified here's the gist:
-Outside battle: Set aside enhancements can be played during prep/discard phases but can only target cards you control.
--Exemption: Territory-Class set aside enhancements can set aside any legal target(s) regardless of when they are played because TC enhancements take full effect whether played during battle or during prep/discard phase.
-During battle: Set aside enhancements, of any class, can be played via initiative and can set aside any legal target(s).