Girlfriend wants to get into badminton, super beginner, wrist pain

Hi all.

I live in the US and want to get my girlfriend a racket, probably on Amazon.

1) She’s a beginner with almost zero experience so no need to spend too much. I’m completely unfamiliar with any non Yonex, Victor, or Lining racket. Does anyone know any budget ones that are decent all in around $50? She refuses to let me purchase it and wants to keep it cheap. I’m thinking of a $30 racket and I’ll take it to the pro shop and have it strung. The factory strings are so bad on these rackets I imagine.
2) She broke her wrist a few months ago and suffers from wrist pain when I got her to to backhand drives. Would it make sense to go head heavy or head light? Also in terms of weight, I imagine finding some featherweight racket like 5U would be best?
3) She doesn’t have much power in her swings so I’m guessing a string like Nanogy 98 that has a lot of repulsion at 23 tension. Otherwise, please give me your suggestion.

Thanks!