Hi there and
to the forums!
Budgies are naturally flighty birds and it's normal for them to be scared of new things.
To get her used to her new toys or perches, put it within view of her cage before you put it in for a few days, gradually bringing it closer and closer to her cage. This works well for my girl, who is also very afraid of new things.
As to her behavior, she's acting very reasonably since you've never made an effort to start at the beginning with her and acclimate her to your presence. You shouldn't ever try to grab her or invade her space with your hand, as you've seen, this only stresses her out.
It's very important that you start at square one with her. Pretend she's a brand new budgie and you have just brought her home: the first thing to do is talk to her, without opening the cage, for as long as you can every day until she no longer shies away when you approach the cage. Just talk softly, sing gently, or read her a story. Her getting used to this could take weeks, or longer, but you must build a good foundation of trust. When she is used to it, you can put your hand on the outside of her cage until she's used to that, and then just inside the door, and then to the farthest corner of the cage, etc. Any time she seems uncomfortable, go back a step. Yes, this is tedious and frustrating, but it is truly the only way to build a lasting and meaningful relationship with this little girl. It won't be easy since she's so scared and flighty, but it can be done.
It's wonderful to have you with us and I look forward to meeting your special girl! I'm glad she was able to be rescued
Meanwhile, be sure to read through the forum's many Budgie Articles and "stickies" (threads "stuck" to the top of each subform for easy reference) to ensure you're up to date on all the best practices for budgie care.
If you have any questions after reading through everything, be sure to ask!