Apparently, the different trumpts are more about ease of doing things than possibility - almost everything can be played on your basic Bb trumpet, even the range now played on piccolo trumpet was originally played on valveless clarino trumpets that were actually longer (and hence had an open bugle harmonic series that began much lower) than a modern valved Bb trumpet. In order to play a full chromatic scale, these instruments were played in an extreme high register where the harmonic series made it possible in different keys with different crooks. I have a friend who specializes in playing clarino, but few modern players master it. At any rate, your range on a Bb is pretty much your range - the issue is the ease and security with which they can be played, and how the fingering patterns 'lay' for a particular piece that determines which trumpet to select. Each key trumpet has a different 'cash register' (the register where most common playing is easily accomplished). Orchestral trumpet parts are traditionally not written in concert pitch, but in the key of the part so it looks like "C" and trumpet players learn to transpose by sight (as do horn players and almost no one else). Because the Bb trumpt is pitched in Bb, it's typically easier to play in flat keys on a Bb - and most band music is written primarily in flat keys because most of the band instruments are pitched in Bb or Eb (flute, oboe, basson, and horn and sometimes tubas being the exceptions). Orchestral music is often written in sharp keys (D is the easiest laying key for the violins), and so orchestral trumpet players 'basic' instrument is pitched in C (concert pitch) because the fingering patterns in the sharp keys lay easier. When a trumpet part is mostly pretty high for a C trumpet, players will often select an Eb or D trumpet so that the range of the music will be within the most comfortable range of the instrument. The timbre of the instrument also is a factor in selection - a higher-pitched trumpet will be 'brighter' all other things being equal.
Thanks for the info. It certainly helps to have a very good ear when playing a transposing instrument.