When reading to someone, we teach our to students simply say, "Would you like to start?" It's quick, polite, and helps them get started right away.
A few of our students play Rock, Paper, Scissors to determine who gets to read first. Of course it is the best one game out of one played!
If students need an additional way to quickly determine who gets to begin, we teach them to roll a die. The student who rolls the highest number gets to read first. It's a nonnegotiable, completely objective way to help students get going on the important business of reading.