A couple of other thoughts.
First and most important (in my opinion) is to have a very vivid mental "picture" (?) of the sound you want to make. One of my former teachers told me that the trumpet in my head needed to be louder than the one I was holding in my hands. If you don't have a musical idea of what you want to sound like, a lot of bad can happen. I know from experience.
Second, and I think you recognize this already, is that you need to take in a very relaxed and natural breath. There should be no stopping of the air flow between breathing in and breathing out - like you naturally breathe. The only difference is that the exhalation is going to have more energy behind it.
With regard to performance anxiety, you may also want to check out a couple of books by Don Greene ( Don Greene Ph.D., Performance Mastery Trainer | Helping Musicians overcome their fear during Audition ).
All that said, one can suffer from 'paralysis by analysis', as I tend to do. Again, I think that it is most important to have a solid musical idea in place first, then go from there. That's just my thoughts - coming from somebody who really is a nobody right now...