Firstly trumpets come in three different 'levels': student, intermediate and professional.
Student trumpets are a good starting point for any player. They are not as high quality, but are easy to maintain. They are usually the cheapest, and so are perfect for a 'student' who may possibly decide that they want to stop playing.
Intermediate trumpets are perfect for developing players who are moving on past the basics and onto higher level playing. I would say they are great for roughly grade 3+ (A great intermediate trumpet is the Yamaha 4335, of which I have done a review here on my blog).
Professional trumpets are for serious players, they are high quality and also the priciest!
Things to think about:
- Set a price limit. Generally, the more you pay, the better the quality.
- Try before you buy. Take the time to try lots of different brands and models to find something that you like. A good tip is to take your own mouthpiece. (If you don't yet play the trumpet, take someone who does - if possible).
- Bore Size. The smaller the bore size, the easier it is to play. Generally, most trumpets seem to have a M/L bore. A large bore will produce a bigger sound, but it will be harder to control.
- Finish. Yellow brass, gold brass or silver plated? Yellow brass gives a warmer sound, gold brass will give a darker sound and silver brass will always be more expensive. (Try out different finished before you buy).
- Teaching book. "Team Brass" is great: http://www.musicroom.com/se/id_no/036824/details.html
- Music stand. A necessity for good posture.
- Trumpet cleaning kit. See my trumpet cleaning guide.
- Tuner. Not essential, but useful.
- Trumpet stand. If you keep your trumpet out of its' case, you are more likely to pick it up and play it.