We generally don't do shopping questions as they get outdated quickly, but I'll post some general guidelines for shopping.
Just about any major brand sold by your local bike store will be of comparable quality within the same price range. Trek, Specialized, Cannondale, Scott, etc. Be careful of online brands as they can be fine but are much more willing to skimp out on certain components to meet a price that they don't think people will notice like lower end brakes or derailleurs.
Don't buy a big box store bike from Walmart etc. Especially because your budget is higher, no user even looking at these bikes.
For tire size I would recommend 26 inch at your price. I recently got a 650b bike and they are still kind of niche, making even things like tubes difficult to find. Maybe that's just the pandemic and lower supplies overall though.
At her height she is definitely ready for an adult size bike, but one of the smaller sizes available.
I would recommend going down to the local bike shops, or calling them up if they aren't open for in person shopping, and explaining what you are looking for. They will be able to ensure that you get a bike of the right size that suits your riding. Call up a bunch of different places just to make sure you aren't getting a bad deal.
Supplies are quite low right now, so I would suggest you get shopping if you want something in time for the spring.