While it might be tempting to sing the first song that comes to mind or a favorite '80s rock song, consider your vocal range before writing your choice on your song slip. Audiences at karaoke bars don't expect everyone to be a trained crooner, but they also don't want to hear you belt out a note you can't quite hit. If you think one note might be too high for your baritone range, ask the Karaoke Jockey or host if the system is capable of changing the key. If they can lower it, great. If not, pick a different song instead of hurting everyone's ears.
It can be a surprising twist for the audience when a singer chooses a song traditionally performed by someone of the opposite gender. Don't limit your song selections to male original performers. That said, if you are choosing a song normally sung by a woman, sing it in an octave you can really sing. Nobody wants to sit through four minutes of your shrill falsetto.
Remember that everyone is there to have fun. If you look nervous and stare at the screen the entire time you perform, the audience will be nervous with you or will be bored and stop watching to talk amongst themselves. Lots of mediocre singers are favorites at karaoke bars because of their incredible energy. If you get up on stage and have a blast, the audience will too. Dedicate your song to a lady in the audience to get more of the crowd on your side. Start slow and let your performance build to keep the audience interested in your Axl Rose impression.
There are some songs that you will hear at least once at every night of karaoke everywhere. "Don't Stop Believing" and "Bohemian Rhapsody" are two of those songs. Choose songs that people are familiar with, so they can lip-sync along, but that they don't hear all the time. Sing a lesser-known, but still popular hit by your favorite artist or choose a song most people have forgotten about but they might not mind being reminded of (think: "Wake Me up Before You Go-Go" by Wham.)