When I have defeated a monster, do I have to decide immediately if that enemy is dominated or a trophy? Or can i horde a bunch of monster cards and decide as the game goes on if I want to turn them in for craft/strength or keep them for fighting?

I think that you must decide right after defeating a monster if you're gonna keep it as a follower (thus aiding you in combat) or if you're gonna keep it as a trophy. Doesn't sound right to keep it as a trophy and suddenly decide to use it as a follower

keith said:

You have to use the ability as written on the card.

Whenever you defeat a Monster in battle, you may dominate it and keep it as a Follower instead of a trophy. The Monster adds its Strength to yours in battle, after which it departs to the discard pile. You may use any number of dominated Monsters during a battle.

The fact that you may dominate it and keep it as a Follower instead of a trophy ensures that you either dominate it or take it as a trophy. You cannot do both at the same time or no one.

When do you take Enemies as trophies? Whenever you defeat them in combat.

When does the Ogre Chieftain dominate Monster Enemies? Whenever he defeats them in battle.

not "whenever you like or see fit".

Sorry for this hairsplitting and nitpicking, I'm just trying to emphasize how Talisman text should be read, in order to be correctly understood.