Java frameworks come in two basic flavors. One is called the "Action" Framework, the other the "Component" Framework.
Action frameworks specialize on mapping HTTP requests to Java code (actions), and binding HTTP Requests to Java objects. Servlets is the most basic of the Action Frameworks, and is the basic upon all of the others are built.
Struts is the most popular Action framework, but I can't in good conscience recommend it to anyone. Struts 2 and Stripes are more modern, and very similar to each other. Both are light on the configuration and easy to use out of the box, providing very good binding functionality.
Component Frameworks focus on the UI and tend to promote a more event driven architecture based on high level UI components (buttons, list boxes, etc.). The frameworks tend to hide that actual HTTP request from the coder under several layers. They make developing the more advanced UIs much easier. .NET is a component framework for Windows. On Java, the popular component frameworks are JSF (a standard) and Wicket.
As a rule, if you're creating a "web site". that is something more akin to presenting information (like a blog, or a community site), the Action frameworks work better. These sites tend to be simpler, get bookmarked often, require "pretty URLs" etc. This is generally easier to do with an Action framework.
Component frameworks are much better for things like back office applications with lots of UI elements and complicated workflows. You'll find, particularly with tooling, that these style of apps will go together faster using a component framework. But component frameworks have more complicated request workflow, sometimes relying on hidden state, lots of POST actions, etc. Many have "horrible" URLs, and sometimes create pages that are difficult to bookmark.
Both frameworks can be used for both tasks, just some are more suited to the task than others.
None of these frameworks directly address persistence, but many have extension modules or idioms that work tightly with JPA/EJB3 or Hibernate.
