You can place them on any card that matches what is described in the special ability. If it says "on a gold Hero" it must be a gold Hero. If it says "a Sadducee" it must be on a Sadducee, but it can go on the black Sadducees or the gray Sadducees equally, or even on a Sadducee that's a Hero, as long as it doesn't say "evil". If it says "a character" you can literally place it on anyone.
Enhancements played during the Battle Phase are played on characters in battle and follow the normal rules of battle and initiative. The only thing that makes TC Enhancements different is the ability to ALSO play them during Prep or Discard on someone in your territory. Heal and set-aside cards work very much the same way, and the placement of weapons on warriors, even though the special ability doesn't work on the weapons right away.