I like the Heimat tone concept of Gerald Webster.
Gerald Webster discovered that when we play a medium high, medium low, medium loud tone on our mouthpiece first thing in the day, the same pitch will come out, our personal "home" tone, or Heimat tone (he discovered this while touring with Edward Tarr in Germany, thus the name). "Personal" means just that, each person has his/her own Heimat tone -- there is no "good," "bad" or "ideal." Just play your first tone of the day on your mouthpiece for a few days, check your pitch with a piano or your trumpet, and you've got your own personal Heimat tone.
Some players start their warm-ups on c below the staff, then work their way upwards, but that makes any thing above c below the staff a more or less a high note. Rather than starting in the lower register, consider starting at your personal Heimat tone and expanding from there. That gives us the feeling of having more low tones to play, and fewer high ones to struggle for. After a couple minutes of expanding from the Heimat tone, you should be in pretty good shape to play.