You will want an excellent sounding pair of headphones, but that's not the whole story about selecting headphones for a trumpet player.
Here are some tips for using these headphones for trumpet players.
You're going to want to use headphones when recording the trumpet for a number of reasons. When we normally play the trumpet, we do this based on the feedback of what we hear. Your trumpet is going to sound different to you while wearing headphones, which is why you want to get over-ear closed headphones. This accomplishes two goals. One is that it will help you hear your musical accompaniment, without the sound leaking out of your headphones (which can be picked up by the microphone).
The other is that you should be primarily concerned with how you sound as heard through the headphones rather than relying on what you are used to, which is how you sound normally in a room. How you sound through the headphones is how you are going to sound on playback of the recording. At the most basic level, the acoustics of your trumpet playing will sound different because you don't hear the sound as it comes directly out of your bell. In your daily life of playing the trumpet you hear yourself as a reflection of the room you're playing in.
The other concern about headphones is comfort. Because you will have them on for long periods of time while you focus on your sound, you don't want a distraction like feeling uncomfortable to get in your way.
You would be wise for your ear health to keep the volumes through your headphones at a low level. When recording, you can produce a custom mix for your headphones to emphasize what is most important to you as part of the accompaniment by adjusting the volumes of the isolated audio and MIDI tracks. Remember to also rest your ears by taking frequent breaks so you don't suffer from ear fatigue.