Question:
am completely guessing but I was hoping to spend no more than $200 -
can that buy a decent bow?
Answer:
It would be far more appropriate for you to "facilitate" her introduction to archery, rather than buying her something at this stage. If you want to stoke the fire, first find her a GOOD JOAD where she can be properly brought to shoot well quickly and safely.
You might, if you wish, provide her with a GIFT CERTIFICATE from the archery shop where the JOAD is conducted - She can then pick out an armguard, finger tab, and chest protector to start with. The other gear - bow, arrows, sight, stabilizer, etc. can all come after she has learned enough to formulate good opinions.