Trumpet

The trumpet or cornet is the smallest and highest member of the brass family. As with all brass instruments, the sound is produced by buzzing the lips into a mouthpiece. The difference between a trumpet and cornet is very minor. They both play the same notes and they sound virtually the same. In appearance, the trumpet looks a bit longer and more slender than a cornet. The real difference has to do with the way the tubing of the instrument flares. A cornet is more cone shaped or conical than a trumpet. For all practical purposes they are the same instrument for beginners. A band teacher may refer to the trumpet section when he or she really means all trumpets and cornets. Either is a good instrument for a beginner.
(from beginband.com)
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Physical Features
While braces are somewhat troublesome at first to a trumpet player, it is not impossible to make good sounds with braces. A slight overbite is okay, but an underbite can severely hinder progress on cornet / trumpet.  Cornet / trumpet players come in all shapes and sizes.
 
Other Concerns
Trumpet parts usually have the melody (recognizable) part, therefore students who choose and are selected for trumpet should demonstrate a confident demeanor, strong personality, and show a high level of self-motivation.

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