A publicity photo ought to grab a viewer's attention, hold it, and show a reason to attend your performance.
Its purpose is to sell your services. It is propaganda, not a portrait. To see the difference, consider this pair of pictures by Yousef Karsh. The first one, Roaring Lion, sold Churchill's leadership to the world. To do so it misrepresented Churchill's personality. Churchill was not stern and scowling—he did not look like a bulldog—he was cheerful and convivial. His scowl was a reaction to Karsh's wordlessly pulling the cigar from his mouth. That picture proved to be one of the most effective publicity photos the world has ever known but his portrait shows him smiling.
A publicity photo needs neither to flatter you nor to match your image of yourself, it needs to make you look good in your field. If your face is going to advertise a concert, the photo needs to make you look like a musician worth hearing. Its purpose is to attract an audience, not a mate.
Instead of supplying several portraits, you are better off supplying one good piece of propaganda. The ideal is to have it become so well known that it serves as a trademark, like the iconic image of Churchill above.
To make you look professional your photo must look professional. It must be sharp, lighted clearly, and fill the frame. It must also be free of the distractions in the background that characterize amateur portraits. Nobody will think much of your picture if it shows a tree growing out of your head.
Common but foolish approaches include standing in a garden or on steps. These backgrounds do not say, "This musician must be awesome." These backgrounds do not even connote professionalism. They might be appropriate for wedding photographs but they are amateurish approaches to publicity pictures that promise amateurism from you. A publicity photograph ought to show you not standing about but doing what you are selling.
A publicity photo is most likely to be printed as a small head shot, but the event's organizers might want to use it as a poster as well. To be maximally effective as a poster, a photo will be not just an insert but the entire sheet, with text printed atop featureless areas of the picture as in the picture heading this page. Your portrait ought to be composed with this in mind.
Any digital camera will record enough information to allow any size of enlargement but if a digital image is ever saved as a JPEG file, much of that information is thrown away. At this point the image can no longer be enlarged or edited much without losing quality. Amateur cameras save images as JPEG files but for professional purposes they must be saved in uncompressed formats: RAW or DNG from the camera then TIFF or PNG from a photo editor on a computer.
TIFF and PNG files are usually too large to email or put on a web page, so for use on the Internet they are compacted into JPEG format. JPEGS are suitable for that purpose but for little else. If an organizer asks you for a publicity photo, email him/her a small JPEG to show what's available but include in your message a link to the original TIFF or PNG. The TIFF or PNG you can keep on Dropbox, Google, or any other server.
For the TIFF or PNG file, the number of pixels does not matter but sharpness does. If you are unsure how to assess sharpness, my photo at the top can provide a standard for comparison. Click the link to enlarge it, then enlarge the browser window it appears in until the photo is the size of a sheet of paper. Compare this to your picture cropped appropriately and enlarged to the same size.