The age of the trumpet and any dents/rust. Though trumpets tend to come in standard sizes, you should make sure prolonged holding it is comfortable. You should try and test play it before committing. And if you're new, don't commit to one too expensive just because its nicer.
When buying a used trumpet, the primary consideration should be the tone or sound quality of the instrument because that cannot be fixed or changed. Also consdider whether the valves work quickly and well, once they have been oiled. Some scratches or minor dents are to be expected but avoid insturments with major damage.
Ask the seller for any repair and service records for the trumpet. The valves might need to be overhauled, the metal might be corroded or cracked. Call around to local instrument repair shops for pricing on trumpet repairs to see what you may have to spend to recondition the instrument.
It should look intact, with no holes or dents. The valves and slides should operate smoothly. There should be no sign of metal corrosion. It is acceptable to buy it if the soft parts made of felt and cork are missing or damaged since they can be easily replaced. You should of course try it out for sound.
You should check if the sounds are consistent since if they have been tampered with , it cannot serve you the purpose.Check whether all the notes sound accurately as they are supposed to sound since they could be worn out or damaged beyond repair and thus cannot be of any help.
First, you should check with the retailer if the trumput is internaly damaged. You should then check the instument for obvious dents, dings, and abraisions.
Make sure it is in good working order. Make sure there are not too many dents in it. You may even want to try playing it to make sure it actually works.
The first thing you should consider is, do you have the money to buy this? Are you going to use it? Or is it just going to sit there and collect dust. Join a school band/orchestra so you will constantly be surrounded by influence to pick it up and use it.