I'll give my 2 cents on this. I have worked with API's in PHP both in SOAP and REST. REST is definitely the easiest to maintain and easiest for your users to integrate with. SOAP requires you to maintain a schema for your API endpoints that is a WSDL file(XML). Any time a parameter needs to change for your API you have to update the WSDL file...not fun. REST is very simple and most people understand it because it is HTTP. I have used this framework: http://www.slimframework.com/ and i like it quite a bit. Setting up the routes is easy and its very lightweight.
If you can manage MVC in PHP you can do a RESTful API.
I will also add this site I found. Its a little more manual that it needs to be, but none the less a good reference: coreymaynard.com/blog/creating-a-restful-api-with…