A lot of things are going to depend on personal preference and what your DD wants to do. Cotton yarn is good for amigurumi because it holds its shape, the stitches are also clearer with cotton yarn but cotton yarn splits easier and has give. Acrylic yarn is slightly fuzzier making the stitches a bit harder to see but is pretty forgiving.
Personally, I don’t really like Stylecraft special DK. I don’t really like the feel of it. I would probably buy a few different brands either by going to hobby craft or a yarn shop. If your DD wants to make something like a headband ear warmer or a hat, go find a nice soft brand, rowan is more expensive but a nice brand for her to treat herself with. A chunky wool is actually quite good to start with (with a bigger hook probably a 6mm hook but it says on the wrapper) because the stitches are bigger and your project grows quite quickly.
For now, avoid any tinsel yarn, avoid any chenille yarn or anything like mohair - this is not forgiving if you need to undo your work. Avoid baby yarn as it’s slightly fuzzier and harder to see. You also want to avoid dark colours like black, navy and brown but you also want to avoid too light such as white, pale pink. Yellow, orange and mid greens and blues are good because the stitches are clearer.
You will need some other supplementary bits - tension ring might help if your DD wants to do amigurumi. She’ll need snips to cut yarn an a tape measure. Darning needles - I like ones that are stainless steel but have an angled end (link isn’t working for me) but if you’re doing chunky yarn you’ll need to find chunky darning needles. Row counters might help. You’ll also want some stitch markers, the locking ones are helpful. If doing amigurumi you might want to get some safety eyes and some polyfill stuffing.
I learnt to crochet like most people here from
Bella Coco tutorials. Knot Monster has some good books with a range of themes and has video tutorials.