Period pants don't need to be tight, she just needs a bigger size, so she's comfy!
Do give her the option of everything, and keep all those options open over the next few years and encourage her to experiment until she is comfortable. Pants, pads, applicator and manually inserted tampons, mooncup, sea-sponge (is that still a thing?).
IME, Mums and peers tend to direct to their preference, whereas your DD might find something else easier and more natural. (Flashback of moving from pads to applicator tampons to manual insertion within months of starting, so much easier for me, but feeling I had to skulk because the general vibe was 'eeewwww'.)
Maybe sit with DD and look at the various subscription / delivery services? Colourful, often have 'new starters' packs, most allow tweaking of ongoing deliveries as DD experiments, and some have add-on comforts like chocolate!
I looked at TOTM a while back, but I think there are quite a few these days. Might be a nice mother/daughter 'treat' way to mark the transition?