1 Don't do monologues from movies.
If you do a monologue from a movie, people will automatically think 'not like in the movie'. That will make them think negative things, and because you're not like the actor/actress in the movie, they'll most likely think less of your ability.
2 Don't do very well known monologues.
Pieces like the 'To be or not to be' speech from Hamlet, or something like that, the directors have seen those all the time. They get tired of seeing that. It's not unique anymore, and they'll lose interest fast. Do ones that haven't been performed enough, or better yet, one you think they've never seen before. It won't bore them to death and they'll like you've taken the time to find something unusual.
3 Do pieces that fit you.
Make sure that your monologue is relatable. Ask people what their first impression of you is. If you get things like 'ditzy popular cheerleader' (sorry, just an example) then a piece about someone like that would be good for you. It looks better than if you do a piece about an old man (unless you're that good an actor) but keep to what others see you as. In theatre, appearances DO matter.