A nice 1/4 is going to have the same characteristics as a nice violin in general, subject to the limitations of the small size. I'd look for responsiveness first and foremost, as that's going to make the biggest difference in technical development. You need good responsiveness across all four strings but at the intermediate level don't need it all the way to the top of the fingerboard.
And the bow is very important.
I've built 1/2 and 3/4 sized instruments, but not a 1/4. We have a particularly fine 1/2 sized violin made by David VanZandt. Sounds like a full-sized instrument, in the right hands, if you aren't in the same room watching it played.
They are out there.
It's good to make sure that kids use good violins in their learning journey, since lessons cost quite a bit too.
btw, what is the range of your 'reasonable amount'?
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There are inherent limitations with the sound when you are talking about a smaller fractional.