I would recommend OpenID Connect.
Too many websites have an OAuth2 authentication API. For a list of the more major sites, see: http://www.gluu.co/oauth-pocket-reference
This is simply un-tenable for web developers. OpenID Connect went final in Feb 2014. Google support it. Any other domain on the Internet that supports it could be supported automatically (i.e. as long as their domain supports OpenID Connect Discovery... publication of their endpoints at /.well-known/openid-configuration
NRI has an open source PHP OpenID Connect library: http://www.gluu.co/oidc-php-rp
If you support these legacy, proprietary consumer IDPs, it will be a pain in the neck as they slowly fall out of favor.
You may also look at a higher level interface like everyauth.com