I'd do Flashpoint R2 TTL Zoom Li-On. It's well within your budget, awesome battery (lithium instead of fooling with lots of AA's), does ETTL & HSS flawlessly, really nice flash, well made, easy to use, and it's R2 communication system so it will work easily with any mixing and matching of R2 lights in the future if she expands and really gets into lighting. It has a built in R2 receiver. Later if a trigger is needed to go off camera, pick up the R2 Xpro controller. Off camera is really great, she will eventually go that way.
They go on sale now and then for about $135 for the lithium version (so wait for a sale):
You can of course go with the standard AA approach too, but I can't stress enough how happy I am to have the lithium battery and not fool with AA's anymore. Then again I use it a lot and I have lots of flashes, so I despise needing to tote 16+ AA's sometimes.
My own anecdotal reasons: I have Canon & Yongnuo and now Flashpoint (Godox) flashes. Lots of them. At this point if I were re-buying everything, I'd fill up on the Flashpoint R2 stuff in Li-On. It's just so convenieint, seemingly endless battery life, fast recycle, the flashes feel great and pretty well made and they're so affordable and have the lovely R2 comm system. Once I got a taste of the Li-On stuff, I couldn't help myself. Huge fan of those batteries. TTL & HSS eats up power fast, so having a great battery and not even feeling the need to have one in my pocket extra has been simply great.