From my experiences in community band
Code:
Crude ASCI bass clef staff. Single dashes denote ledger lines.
Notes are in concert Bb. (numbers are fingerings)
-Bb (0)
A# (0) A (2)
-G (12 or 3)
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-
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Fb (123 or 24)
-E (123 or 24)
For the lower end, some euphoniums do not have a 4th valve, so if pieces going below the E below the staff aren't really a thing, or in the rare case it's there, go up an octave
For the higher end, The G above the staff would be an ideal minimum (I'm thinking in particular the euphonium solo in 2nd Suite In F, 1st movement, by Gustav Holst). I've had to play very brief passages involving A and Bb above the staff. This was for someone who 'wasn't that great'. If instructors know you're more capable, you can expect to go up to 2 half steps above the Bb