What would you suggest as a good and practical but simple pattern for a solution with JSP/Servlets + EJB + MySQL
Use the MVC framework of your choice, Stateless Session Beans for the business logic and transaction management (prefer local interfaces if you don't need remoting), Entities for persistence.
Inject your EJBs wherever possible (if you are using Java EE 6, this means anywhere and you can also skip the interface).
And is it necessary to use an own layer of DAO for persistence? I use JPA to persist objects to my DB.
Some might say yes, I say no in most cases. The EntityManager
already implements the Domain Store pattern, there is no need to shield it behind a DAO for simple needs.
You might want to read the following resources for more opinions on this:
Should I withdraw business logic from my EJB?
I wouldn't. Put your business logic in your (Stateless) Session Beans. EJB3 are POJOs, they are easily testable, there is no need to delegate the business logic to another layer.