Including a file on every page in a module
If the file needs to be included on every page, the correct way is to use PHP's include or require, I don't think the fact that this is in a Drupal site should really make any difference.

I've seen plenty of modules that literally put the following at the top of the module file:

require_once('module.inc');
require_once('test.inc');


If you really want to do it  a 'Drupal' way, you can use module_load_include() (which just wraps around require_once internally), directly at the top of the file instead of inside your page callback. This is what I tend to do normally.

module_load_include('inc', 'MYMODULE', 'MYMODULE.something');


Adding the file in hook_init() is perfectly fine too, I can't think of any justification to use one over the other, it would be down to personal preference.