In Java you have actually two ways to start your design of your web service. You can either create the WSDL (Web Service Description Language) contract first (contract first approach) and then let Java or some framework tools create Java skeleton classes for you which you can use to implement the logic of each operation or you can start by code first approach and implement each web method and its logic and then let Java or some external framework tools generate the WSDL contract for you.
Either way you start, the result should be very similar and platform independent. The standard message format used for WSDL based web services is SOAP (Simple Object Access Protocol) which is based on XML (eXtensible Markup Language) which is by definition platform and programming language neutral.
So, after implementing your service and starting a server for the WS endpoint adding ?wsdl
to the end of the endpoint URL should return the WSDL contract to the invoker, which can be used to create client side stubs for the required programming language which furthermore simplify the sending and receiving of messages from and to the web service. Note however that creating stub files might not be needed as all the information may be parsed from the WSDL contract directly. As of lack of knowledge concerning PHP I can't give details on how to call a WS from PHP directly or if stub file creation is required/recommended.
In order to call an other WS from your service you need to create a WS client within one of your web methods and invoke one or more of the operations offered by the remote WS and process the response within your web method.
As I am not sure if you are using any (Java) frameworks like f.e. Apache CXF I am not giving any code examples here. For integrating external web services within your service you might also have a look at Apache Camel which offers integration support for numerous Java based frameworks including CXF. Here your web service is treated as a Consumer
while other external services you need to invoke are handled as Producers
. The interaction between your internal and the external services is modeled here within a route where you can apply various Enterprise Integration Patterns (EIP) like splitting multiple elements contained within a response into distinct objects which you furthermore can process in parallel.
In general your enumeration of steps involved does look right if you follow the code first approach but as mentioned earlier you can also start by defining your contract first. Depending on your knowledge of the WSDL/XSD syntax (the less you know the exact syntax the more you should use code first approach), crating the contract first might enable PHP side integration sooner while you still develop the internal logic of your implementation.