Regardless of issues with the rescue- Anatolians are a livestock guardian breed. They are intelligent, independant, and have guarding instincts. This is a breed that has not changed much since it has been developed. Because they are working dogs by nature, they do best with a job. You will have to work hard at training with her and ultimately, if you can't give her any job to do (a job can be come outside and sit while I let the chickens out- it doesn't have to be fancy, just give the dog a sense of purpose), I don't think that this is the breed for you.
It sounds like with this specific dog, she's had some behavioral issues develop (probably due to poor ownership originally- if you get a guardian breed and don't train it well, no wonder guarding issues have developed!). Unless you are willing to work through those issues, and possibly have a very hard time because of the breed's independence coupled with intelligence, she may not be the dog for you. It'll also be a bit of a shock if you've only ever dealt with breeds like retrievers or other very biddable dogs- I am fully immersed in the world of dog training and I wouldn't want one unless I wanted a guardian dog. If you have experience with other guardian breeds, or something like huskies, malamutes, or german, dutch, or belgian shepherds, I probably wouldn't go for it unless you're very confident in your training ability.