As much as I love my jazzmaster they are hard work and could put off a beginner. Mine is so rickety, it really exaggerates my awkwardness as a guitar player (although a positive byproduct of this is that i’ve developed quite a delicate guitar style that I don’t think I would have on a more ‘all rounder’ guitar), the problems with the bridge are like a whack a mole, fixing one problems causes another one. Ultimately they are worth the effort and the things they do well they do better than other guitars, but probably best when someone is drawn to them.
How about a mustang? A happy medium between jazzmaster/jag and strat (plus short scale might be better for children hands), although if they want a strat that is probably what will inspire them the most.
I think squier are fine, definitely on par with cheaper fenders. I have the Bass VI which is incredible value for money, I briefly owned a squier jag and it was good (only got rid of it because I prefer 7’25 neck radius but even fender have ditched those on their offsets now)