Inhale fully to a comfortably full level. Maximal inhalation is used for emergency situations. Your body can lie. For example you can move chest and abdominal region and not inhale. If you want to move tissue you can order body to do this-or you can order breath.
Brass instrument is for resonance only.
Player supplies vibration and air. You are built to survive and use muscles as systems not individually. Timing is secondary to quantity of air. How much counts for more than how long it takes to get breath. Use arm to tie in a physical feature with respiration.