I have a simple REST JSON API for other websites/apps to access some of my website\'s database (through a PHP gateway). Basically the service works like this: call example.com/f
OAuth is not the solution here.
OAuth is when you have endusers and want 3rd party apps not to handle end user passwords. When to use OAuth:
http://blog.apigee.com/detail/when_to_use_oauth/
Go for simple api-key.
And take additional measures if there is a need for a more secure solution.
Here is some more info, http://blog.apigee.com/detail/do_you_need_api_keys_api_identity_vs._authorization/