My students use Kala KA-15S sopranos (~$70). They’ve held up well over the past five years of regular use.

I personally have an Ibanez soprano, an Islander “super-tenor,” and an Ohana Tenor (acoustic-electric). Both tenors are strung with a low G (I wouldn’t do that with a soprano). My favorite is the Islander super-tenor, but I don’t think you can get that one anymore.

If you just want basic ukulele, go for the Kala. If you want a slight upgrade, go up to a “concert” size. I wouldn’t go any bigger than that until she’s older and has a better sense of what sound she wants. If you’re willing to pay a bit more, I highly recommend the places that will do a “set up” for you. I got my Ohana online from Mim’s ukuleles. She took great care of me! I got my Islander online from Uke Republic. Both offer “set up” (checking the action, fixing buzzes, sanding sharp frets, etc.).

There are lots of price points. You can also check out the reviews online.

Get a tuner (Snark on Amazon is $10) and a bag. I like using a strap, but that’s a very personal preference.