Moving to Birmingham

Hi friends,
We are (family of 4, 2 adults, 2 children Protected content 10) are moving to Birmingham from Singapore.

Wanted to get some idea of cost of living considering the cost of schooling, commuting and living expenses. Some friends have recommended areas such as Edgbaston, Solihull etc to live. Any comments, recommendations would be helpful to make our plans and decide.

Especially if someone can provide insight into Private schools vs. public / grammar school would be immensely helpful.

Thanks in advance.
Sachin