Reference request: Arithmetic circuit complexity
This depends on what you want to do. For more structural questions there is a relatively recent survey by Meena Mahajan:

Meena Mahajan: Algebraic Complexity Classes. 

There is also the book by Bürgisser:

Peter Bürgisser: Completeness and Reduction in Algebraic Complexity Theory.

For Geometric Complexity Theory, you might try the theses of Joshua Grochow or Christian Ikenmeyer. I think both of them have introduction into the field, but I must admit that I have read neither of them.