You're starting out in music with a dream of playing the trumpet, or your buying a trumpet for a beginner and all of a sudden it's information overload.
Let's get some things clear from the off.. if you're going to play the trumpet you will have a Bb trumpet, despite all the other models out there (C, D/Eb), whether you get a student, or professional trumpet this is your staple trumpet. It is the most common trumpet used in the world.
But was does Bb mean? Quite simply, when you play a 'C' it actually sounds a Bb. This relates to 'concert pitch'. Instruments such as the piano, flute, oboe, and stringed instruments play at concert pitch; they play a C and it really is a C.
In fact the vast majority of wind instruments don't play at concert pitch! In addition to the trumpet, this is the same for most other brass instruments, and also clarinets, saxophones and Cor Anglais. Now while this may seem complicated, it is actually to make life as a musician a lot easier. If you were to unravel a trumpet it would be a long tube. On that tube you can play a series of notes; make this tube smaller you would be able to play notes of a higher harmonic series. This is the same for all instruments; the longer or shorter the instrument, the difference in range. However, when you change the length, you change the notes. If you had to learn different fingerings to play and sound a C for instance on all the harmony instruments you'd have quite a job; it's much simpler to use the same fingering on all the instruments and just change the notation of the music instead. (This is why if musicians tried to read the same music when playing instruments in different keys would sound off!, so each piece of music has to be written out in the right key for the instrument).
So why don't they make instruments in the right length to play the right note? Well actually you can find C trumpets, saxophones, clarinets, but because the length of them is different to their standard models, they produce a different tone and often can actually be more challenging to play. Music is all about sound and when you pick up an instrument you strive to make the best and most pleasing tone audibly possible, which is why over the many years of musical instruments, a standard has been set for instrument keys, which is why amongst many other brass and wind instruments you'll find a trumpet in Bb!