How to choose an audition piece
Start with the basics. What is the audition for? If it's for a particular play research the director and writer, see what kind of style they usually work with and try to work with that, for a simple example if it's a Shakespeare play then do a Shakespeare monologue. Try not to choose a monologue from the play, or from anything that the director has worked on before. Identify what you like about the kind of work they do and choose something similar.
If it's a drama school audition then you need to choose your range. This doesn't necessarily mean dramatic vs comic: this could be a character actor piece and a straight piece, or more specifically a vulnerable, dry witted modern piece and an energetic farcical classical piece, whatever works for you.
When choosing monologues I have always found that it's best to go for a simple, personal option. Try to find a piece which, out of context from the play and character, you can relate to: one that has a subject matter which YOU want to tell people about. If the words speak to you and make you feel something, or make you think, then the chances are that when you perform them that connection will shine through. Of course it's imperative that you know the character and the play for reference, but remember that an audition panel (especially a drama school audition panel) is looking to see who you are, and to see your vulnerability as well as your strengths. So if your strengths are in comedy and you find a piece that is funny AND moves you, then go with that.
In terms of looking for an audition piece, start by reading lots of scripts that you actually want to be reading. Monologue books can be over used and the best pieces are found by accident.
If it's Shakespeare, everything is over done. Try to approach the text as a piece of new writing, that's the best way to come up with a more personal version of the monologue, and stay away from the really epic pieces ('To be or not to be..') because those pieces need a lot of work to perfect, even when they are being done by the pros.