$750 is a pretty high budget, so opens up a world of options. That's actually the highest I've ever paid for a snare. Most of mine have been in the $350 - 500 range. Some shells will have a naturally lower tone than others, but tuning low is more of a technique than the shell material. Obviously shells with a lot more high overtones don't help with the sound, but high overtones can be tamed with heads, gels or even something like a Big Fat Snare Drum
I was covering for a band last year that played a variety of songs. I covered the thuddy classic rock songs with that. Just through it on before the song started and removed it after. Some snares are happiest in a particular range, tuned high, mid or low and suffer at one of the other ranges.
This is where the workhorse snare should excel in. A Ludwig Supraphonic (aluminum) is probably one of the most recorded snares, especially for older recordings, followed but the Black Beauty (COB). I don't have either. They are way too pingy for my taste, but I'm pretty lonely here with that preference, but having said that, I only use single ply heads on my snares, which are pretty pingy. Already getting deep in the weeds with drum geek talk, which will serve to add confusion. The Drum Center of Portsmouth, Sweetwater and Memphis Drum Shop videos I recommended earlier all use the same single ply heads to demo their snares. That'll give you a good feel for what the drum will sound like if played wide open (no muffling). They also show the snares in low, mid and high tuning, so you can really get a good feel for how that particular snare may sound in the genres.
I've used those sites pretty regularly. Having said that, I bought a Tama Starphonic Bubinga a while back based on those videos, because I was really looking for a nice deep sounding drum. It was fantastic. I then bough my Gretsch USA Bronze, which ended up having an even lower and warmer natural tone than the bubinga! I wouldn't have guessed that. Wood is always lower than metal right? The bubinga was still my go to for the high cracking sound, just so I didn't have to retune the Bronze, but the bronze did that better too. I still liked the bubinga for the dryer sound, but then bought a cast aluminum snare, which is dry and can cover the same ranges as the bronze. So my bronze ends up covering low to high with more overtones and my aluminum for less overtones. That has put my bubinga snare in no mans land for me. Just a beautiful drum with fantastic hardware, but I can o both lower and higher with the other two. The Bubinga is still king when looking or a lower volume snare. It's a very "polite" snare, so has its place too.
There's trial and error with just about all instruments. So far I've knocked on the Ludwig Starphonic and Black Beauties and than ruffled additional feathers with taking a whack and the Starphonic Bubinga. I'm now looking for a place to hide to avoid the scorching that is about to take place!
In all seriousness, I'm just trying to point out, it's a tougher search than you may think and YouTube will help reduce confusion a ton. That said, how a drum really sits with one's tastes and expectations is still a matter of preference, so no holy grail. There are more common choices, which should get you at least close and go from there. I'd also highly recommend going the used rout. Love the $750 budget for when you know you're a 100% on a snare. Get them used, have your daughter play them for a bit, if she doesn't take to it or decides she's looking for something different, resell and get a different one. The new $750 snare will be worth 50-60% of it's value used, and there's going to be tons of experimentation in the days/months/years ahead. You could be flipping $400 used snares weekly without losing much, especially, if no shipping is involved.