Web Service implementation on the client
Looked briefly into your program, here are few points:


  I would like to know whether or not my web service example method is
  suitable for client-side implementation


Web Client implementation doesn't need the actual implementation, if the service is hit able, it's client can surely be written. 

addProduct(String name, String genre, String platform, String developer, String publisher,
int ageRating, double price, int quantity, String description)


Why not create a Product bean and pass it instead of so many params?


  (I have been creating basic web services using the axis2 framework and
  running them on the Apache Tomcat server. However, I am open to any
  suggestions or recommendations in regards to alternative servers and
  frameworks.)


This seems fine but from the learning perspective, give Jersey a try.