Take into consideration the size of the venue and the acoustics. The music should be a compliment to the event, not too overpowering. Chances are that if other people have been pleased with the musician you will be too. Don't be afraid to ask for and check references of the performer you are considering. Audition whenever possible.
Auditions can be in person, over the phone, by tape or video.
Audio tapes let you sample the style and expertise of the musician. Video additionally allows you to see the appearance of the performer. Make sure you like the quality of the music and that it is appropriate for the event. Give the musicians your musical requests. If you have a particular selection or selections you want included be sure to discuss this in advance with the musicians so they have time to get the music and rehearse.