Oy vey, where to begin?
Two elements here:
1. composing the music
2. orchestrating for big band
Your questions seem to ask about element #1, the actual compositonal process, so I'll address that here.
In short, I'd suggest writing whatever comes to you first, be it a chord progression that you like, a good melody, a catchy rhythmic groove, a unique textural setting, or something else.
The challenge I often find is rounding out the elements of a tune. So, if I start with a cool chord progression or vamp, I try extra hard to write a good melody to fit with the accompaniment — otherwise the melody is just a throw-away.
Conversely, if I start out with a purely melody-driven work, I spend a good amount of time looking for "the right" harmonic or modal setting.
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Orchestrating for big band, now, is a different set of discussions.
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have you written any of your own "tunes" that you might play with a quartet, for instance?
~Rick