Production of Audition
Even though, above all else, the casting director(s) is searching for talent, recording a quality video of your audition will aide in your overall appearance and professionalism, and especially help with sound quality. Because this is a music audition and your voice (or instrument) will ultimately be considered above all else, it’s best to use a good external microphone, although some cameras do already feature good quality microphones.
Consider the placement of the microphone. If you’re using a boom microphone (aka shotgun mic), have someone hold it just out of frame, either above or below the talent.
Or, if using a unidirectional cardioid, you may decide on even placing the microphone in the shot and have the talent sing directly into the microphone.
Do a couple of test runs until the levels sound right. If there’s a good bit of raspy-sounding pops, consider using a wind screen or ‘spit screen’ (pantyhose stretched over the microphone does help with eliminating popping sounds and does make the human voice sound smoother.)
Or, in post production, use a sound filter to eliminate the popping (most non-linear editing systems have audio filters). If at all possible, it’s better to fix a problem when shooting.
Choose a background that’s not too distracting. Keep it simple. This is a music audition, therefore it’s the talent being considered, not the production design. Do you really think the casting director will care about the placement and color coordination of furniture in the background? No! Therefore, there’s no reason to spend money on a set! Use what you already have. However...
The lighting does need be considered. For instance, if the talent is seated in front of a bright sunlit window, use lights so that the talent won’t look like a shadow. If you have the time and resources, use gels to set the color temperature with the daylight outside (or, color correct in post production). To see basics about lighting, read here.