Just as a matter of clarification:

When an effect instructs the first player to "choose a character/hero" it does not have to be one of his own heroes?

This comes into effect under such circumstances as Arwen´s (encounter card version) ability to place resource tokens, first players job to attach cave torch to a hero of his choice, Durin´s Greaves which must be placed on a hero of first players choice etc

Nerdmeister said:

Correct.

Generally, the first player can choose any applicable character/hero as the target for such effects. The only restriction involves costs (cards with the "pay X to do Y" structure, such as Strength of Will, Protector of Lorien, etc.). A player--any player--can only pay costs with cards he or she controls. Otherwise, the first player usually has carte blanche when selecting targets (taking into account any restrictions stipulated on the cards themselves).