Hi, I've lived in Liverpool all my life.
I'd probably recommend to live in West Derby, reasonable house prices, naice area, near Alder Hey hospital and bus links to South Liverpool secondary schools. Also can't go wrong with Childwall, Aigburth, Allerton, Woolton. Some parts of Halewood are nice but it's hit and miss, but you'll get more for your money there.
When looking at primary schools look for which secondary schools they feed to, the best secondary schools for girls in Liverpool are; Bluecoat (grammar), Kind David (Jewish, St. Edwards (Catholic), St. Julies (Catholic all girls), Belvedere Academy (Former private all girls), Liverpool College (Former private, v hard to get in to).
All are South Liverpool except St.Edwards which is in West Derby.
I attended Childwall School and Broadgreen International a few years back, both schools had good points but I wouldn't recommend either.