When/where to include my own function library (like common.inc)?
Probably best to put it in it's own custom module, e.g 

sites/all/modules/custom/mymodule_common 


and enable it as required.

You can make it a dependency of other modules by adding it to those module's .info file, e.g

dependencies[] = mymodule_common


You could also use subfolder and standalone file in sites/all/libraries/common though the module route is recommended.