Okay, I play four instruments, piano, viola, violin, and irish flute (which includes the whole flutes, whistles and recorders thing as well). Here's what I have come to find:
Piano gives you a good sense of what notes are what, quite quickly. It also gives you a sense of when notes are in tune or not (which is helpful for the next two instruments in the list). You also learn Treble and Bass clef at the same time, so that's already two clefs done.
Viola tends to have a rich sound, and then rest has already been said in previous posts, so I won't go further into that. With viola, you start with the alto clef (aka C clef), you learn it, and then you normally get treble after a few years of playing. So you get both clefs fairly early on, which helps in later on, but I'll get to that later.
Violin tends to have a high and painful screeching sound when played by an absolute beginner (you get that with viola too, but it's not as painful). This is normally overcome within a few months. But then you have the higher notes in higher positions which, when played by the common beginner, are extremely painful. They are just high and shrill and such, so it hurts.
Lastly, for the original question, if you intend on having her do both ITM and classical, I would go with viola first. Violas are very needed in almost every orchestra around the world, so there would be plenty of orchestral opportunities for her, but violins, well, there are plenty of them. Eventually, you would want her to do violin as well, but it will be much easier than doing viola second because she will already know the clef, and will easily become fluent in both instruments. The biggest hurtle in this situation is the string changes, which I got over in about 15 minutes. Also, when it comes to fiddle tunes on the viola, I do them a fifth down, because if you do them an octave below, it doesn't have the same fingering and bowing as fiddle, so 1, you can't switch back and forth between the violin and viola with the same tune, easily, 2, the phrasing and such will be wrong, and 3, the whole thing will just feel wrong, and it won't want to flow as easily. So, if you're fluent in violin and viola, you can read the violin music, and play it with the exact fingering and bowing of a violin, on viola, and it will automatically transpose itself! Then it's your job to get a G whistle and play it as explained in an earlier post. Hope that made sense!