A used play as in plays that have quot;alreadyquot; been preformed by others?Can you do both?
What do you mean 'at Broadway'? Do you mean for an audition? If so, you should always perform (not preform) a monologue from a published play. If you mean what plays are performed there - the answer is all sorts - ones recently written by fairly new writers, but these will all have been performed in smaller venues first, as a test run to see how audiences liked them. Also established ones by well-known authors. Very few actors write their own material.
First you must become the character from your heart. Does it matter whether or not what kind of plays you can or cannot use? As long as you are able to perform a variety of characters and are still able to be yourself, then the taking on a character, whatever the form, will not be too difficult. It is always good to write plays to understand the sets and detail analysis, which will help you in the performance of acting. however, performing your own pieces should not be necessary.