How would I allow a simple PHP site, which already has a user db, to let Drupal handle the logging in of users?

My thoughts are (a) services module and (b) making drupal an openid provider. I haven't got a clue where to start with (a) and am worried about confusing users with (b) - there can't be any "openid" branding, the users should simply log in at the drupal site and be redirected.

The main priorities are that the user should only have to log in once for both sites, and the existing users on the external site can be maintained and transitioned smoothly. I want Drupal as the main user db because it's more secure and I think it's easier to have the external authenticate off Drupal rather than the other way around.

Any thoughts? Thanks in advance.