This thread has amazingly long legs -- and is quite interesting to me, particularly in terms of the remarks people make about starting in one clef and switching to another. This seems to be the biggest worry: that is, the difficulty of doing this. In part, however, it's not just learning the new clef that's the challenge, but (since you're essentially switching from a transposing to a non-transposing instrument in the case of euphonium), you have to learn new fingerings. Some people seem to find this more challenging than others, but I do think that it is never really a significant problem. And as has been remarked already, keyboard players are expected to learn two clefs simultaneously (though they don't have the new fingering issue exactly), and I've know trombonists who seem to play in more clefs than I have fingers (again without new fingering issues, although if you go for alto trombone you face something similar).
In my own case, I trained for almost fifteen years as a saxophonist. And certainly a major reason for the saxophone family being composed of transposing instruments is the ease with which a player can switch from one variant or another (if, for example, the bari sax player gets the flu). And a lot of saxophonists will regularly play two or three of the variants. Among all those, only the C Melody saxophone is non-transposing and produces a C when you finger a C -- and no one plays that nowadays anyway. When I decided to pick up a second instrument, it was the flute. In part this is because I like the flute, but in part it was because of the similarity of fingerings with the saxophone (somewhat more similar than the clarinet, it seemed to me).
Decades later when I decided to become a low brass player and acquired a 4-valve Eb tuba, I learned bass clef for the first time in my life, and I recall it taking only a few days to get it down quite well (okay, maybe with the exception of the more distant ledger lines, but that's a problem whatever clef you're in). When I changed to a BBb horn several years later, I then needed to learn "new fingerings", and this took a little more effort (it seemed), but not much. A couple of days? A similar experience when I acquired a euphonium. Even though the fingerings are "the same" as on the BBb horn they are unfortunately "at different places" in the staff . I am now in the hunt for another Eb to add to my stable and expect to pick up the fingerings again without undo difficulty.
My point here is that while there may seem to be a number of concerns about what clef to learn first, and the difficulty of switching clefs (and essentially switching from a transposing to a non-transposing instrument), in practice this won't really matter and I would guess that any reasonable student could make a passable switch within a week or so, and a very competent switch with just a bit more time. So not to worry. I do confess that since I started playing low brass, the bass clef seems to me to be the "natural" one, but all of that is a matter of habit and there is nothing more natural about it than any other clef. This is a lot like learning to speak or read different languages (well, it is learning to speak or read different languages). But the languages in this case are really simple. Not at all l like the time I tried to learn to read Polish by myself. This whole clef thing is pretty straightforward.
Also, it will ease interaction with the band/music teacher to continue with treble clef at this point. And why complicate that, especially for a beginning student?
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)