I'm thinking about getting a trumpet to practice at home for fun. I want to know what type of trumpet is best for me. I'm in 4th grade and need something to do at home. I need to know the difference between the different types of trumpets, too. I am a beginner and know nothing about the trumpet.
First thing to do is find a teacher who can explain things a bit to you. And you absolutely will need a teacher or you'll give up in complete frustration.
Obviously you don't want a medieval straight, valveless trumpet :-) .
Your basic choices are either a trumpet or a cornet. They look almost the same, but the cornet is a bit easier to start out on and is slightly less strident/brash in sound. Then there's fancy stuff such as the flugelhorn or Drum&Bugle Corps-style marching bugles. Leave these for later.
In all likelihood you can find samples of all these variants on YouTube.
Bb trumpet (or cornet) is the near universal standard for beginners.1,2 Trumpets are often marketed as "beginner" or "student" models, so that would be a useful way to search, and you needn't know much more. You might do some research on the quality of different brands.
For someone who wants to get off to a solid trumpet-geek start, however, there are a couple of basic factors that differentiate one trumpet from another.
Perhaps the most important part is the mouthpiece. Mouthpiece sizes are based on how big around they are and how deep the "cup" (the part you blow into) is. A smaller-around, not too shallow or deep mouthpiece is typical for beginners. Student trumpets will generally come with student-sized mouthpieces, so you needn't worry about shopping for these yourself; it's just something worth knowing.
Another differentiator is the "size" of the trumpet. Although Bb trumpets are all the same length, there can be variations in how wide the tubes or the bell (where the sound comes out) are. Trumpets with slightly narrower tubing tend to be easier to blow and so are common among beginner instruments. As trumpets get larger (and heavier), the sound becomes a bit more mellow, but harder to produce.
1 "Near" universal only because I have to allow that some school somewhere asks their students to use something else.
2 "Bb trumpet" means that if you could unwrap the trumpet so it was a straight tube, the basic sound you'd get would be a Bb. There are other kinds, but they are generally for specialized purposes.
You need a Bb Trumpet. If you're offered a Bb Cornet it plays almost exactly the same. If you're aiming to join a certain band (and trumpet on its own isn't much use or much fun) contact them now. They'll doubtless have a training scheme, maybe even an instrument loan one. At the very least you'll get good advice and some contacts for obtaining second-hand instruments.