Every actor should have at least two contrasting monologues performance ready at all times. But it will behoove you to have more choices than that. You'll want pieces that are the best representation of your talent and that can be used for several different types of auditions. How should you go about finding what works best?
Do Your Research
Doing an online search first is fine to start. It can give you some ideas to jump off from. But spend a day at somewhere like the Drama Book Shop and read through monologue compilations. Take note of what pieces resonate with you and find the full length plays they are from. Also, think of plays you've seen that you've liked. Note the author and check out the script for that play as well as other plays by the same author.
Read the Entire Play
While a one-off monologue is fine, it is much better to choose a monologue from a full length play. A play does most of the background work for you; it puts you in the location, introduces you to who you are speaking to, and gives you everything leading up to that moment. Once you have found the monologue, read the entire play it is from. Every page will give you clues into your character and help flesh out the moment you are performing that much more.
Have A Variety
A monologue that combines humor and drama all in one is great to have and you should look for contrasting moment in each individual monologue. But having different monologues for different auditions is beneficial. For example, you wouldn't perform a dramatic monologue about losing your child if you were auditioning for a slapstick comedy. Also, once you get in front of potential representation, you'll want to show them your versatility. This can be done through performing monologues from very different genres.
Monologues should be no longer than 2 minutes. Some auditions will even want monologues that are one minute. Have a variety of lengths within your repertoire. Ask a professional for help editing down monologues (except for classical monologues) to fit a shorter time length but make sure to keep important information to keep the piece moving forward.
A Fresh Take
Try to find a monologue from a lesser known play if you can. It will be a new story that perhaps your auditioner hasn't heard yet. However, there is nothing wrong with doing a monologue from a popular play. Just make sure to make it your own and make bold choices. The auditioner may have heard the words before but they haven't seen your interpretation.
Shakespearean and classic monologues are very different from contemporary monologues. If you are auditioning for anything in the present day, do not bring in a classic monologue. However, it is very helpful to have at least one in your repertoire. Since there are no more "classics" being written, the monologues are of a limited number so the chances of you performing a popular one are high. You can still have "a fresh take" on it and present it through your lens. Study with a teacher strongly versed in the classics before choosing a piece. They will be able to help you navigate the language.