How To Pick A Good Monologue

It must mean something to you, you must be able to relate and connect to it in some way. Never pick a monologue because there is a deadline coming soon, you must take your time.
It must make you excited to do, if your doing something you are forced to do, or really want to do, then it will never be as good as it could be.
It must have a sense of a clear acting partner. Who you are talking to: your Brother, your Friend, your Mother, who? You must make sure you know.
It must have a clear objective. What are you fighting for? what do you want to do to, or get from your acting partner? Make sure you work your objective always.
Always try and avoid the "story monologue", that is a monologue that tells a story.
If you chose to pick a comedic piece, make sure you are funny! Remember, comedy is a lot harder then you think.
Do not chose a monologue with a lot of profanity, although you may think it would be a lot of fun to curse your mouth off, to much profanity will draw attention off your acting skills and bring the adjudicator just to pay attention to your profanity.

How to pick a good scene

Never do anything too overdone! A good way to find out what has been overdone is to pick up your schedule from last year or the years before and see if you see it. If this is your first year, ask a friend. If you don't have a program, ask people who are very informed with theatre. (Remember, I am always open for any question that you may have)
Make sure that the scene (like the monologue) means something to you. You must have a passion for your character.
Make sure you are working with someone that you like, or at least can deal with. If you don't like working with your acting partner, the process can become very nerve racking!
Don't pick the first scene that you find. You should view many scenes and read many plays to find the scene that suits you well.
Make sure the work is with-in your acting ability. (For example, if i was a beginning actor, I would not choose anything from any of Shakespeare's works)