Wow. What a great question. My suggestion would be to put "tone production" ahead of everything else. My approach as a beginning band teacher for 32 years was to have students work on their "tone producer"* until they could play a big, clear, beautiful sound before they ever touched the assembled instrument in class. This involved learning the correct breathing, breath support, posture, and embouchure.
Once they got the required sound on the "tone producer" then they were allowed to move on and "amplify" that sound through the entire instrument. We would then start with a big beautiful sound on just one note on the instrument, and then add one note at a time until a scale could be played with that beautiful sound. Once a scale was mastered, then tunes could be played using the notes of that scale. If ever the tone quality started to suffer, it was back to the "tone producer" for that individual player to brush up on the tone production fundamentals.
Most other beginning band teachers would go through 2 or 3 band books in the time it took my classes to go through 1, but the difference in the tone quality of the groups by the end of the year was obvious . My philosophy has always been, "What good is it to be able to play lots of fast notes if those notes don't sound good"? The speed and technique will come eventually with practice, and the notes will sound like "music" when they do.
*sax - mouthpiece and neck
*clarinet - mouthpiece and barrel
*flute - headjoint
*brass - mouthpiece