Lot's of stuff to learn in here so I would take it a bit at a time. I'm going to assume you are relatively comfortable with the Java language and core APIs.
First learn about JDBC and databases. Get a basic functional JDBC example app working (not visual just some a vanilla Java app) that does read/insert/update/delete of some records in a table. This will give you the basis for building whatever app you choose. Almost all interesting applications involve some sort of persistence/database.
Learn the main JDBC APIs (Connection, PreparedStatement, ResultSet) and write some code that uses these to get comfortable.
Learn about how transactions work in databases if you aren't familiar already and how JDBC uses them (Connection.commit and rollback)
Next you could look into the spring framework. This has a several useful features that come in handy when building these applications. The main ones to get to know the dependency injection functionality and the JDBC libraries it has. The DI stuff is a bit of a "duh"? if you haven't used it before but it is very useful/powerful especially for medium size + apps. The JDBC libraries help with the cruft of dealing with the raw JDBC APIs and make your code less error-prone.
Once you've got some basic JDBC and Spring stuff worked out you can then start bringing in a web framework.
This is more difficult because there are so many. In the interest of getting something up and running quickly I would probably go with Wicket. It runs inside a servlet container like Jetty, easy to get up and running with a basic web page or two and relatively easy to evolve of the project over time without going down too many blind alleys. I've found that frameworks like JSF (the Java EE default web/view framework) takes a lot of up front time investment to get going on. Most of these frameworks, including Wicket, can leverage the spring stuff you've got above.
Avoid JSP, it's unpleasent technology and outdated by virtually everything else.
To answer some of your other points.
Hibernate is a tool for mapping an object model to a relational model. In it's most basic form you define a Java class for each DB table with the class having one Java property (variable+getter+setter) for each DB column. You can also add references from one class to another to model database relations. It is good but it takes a bit of getting used to.
Spring I've explained partly above. Spring is much bigger than just DI and some JDBC libraries. It also has transaction management libs and bunch of other stuff. Spring MVC is a web framework which lives under the spring umbrella and makes use of a lot of the spring libraries internally. I've never used it so can't offer an opinion on it.
Java EE is an umbrella term for a large set of "enterprise" specifications/libraries. JSF is a web view framework that is part of Java EE.
That's my very high level advice. To summarise I would learn basic DB/JDBC then some spring stuff and then start building a basic web app using what you've learned already.
Hope that helps. There's plenty of info out there on the web on all these topics and you can always ask questions here on more specific parts if you need help. Good luck and enjoy!
EDIT (to address comment):
All of the above is my recommendation/opinion on how to approach learning Java web development.
In summary
- Learning JDBC/transactions/databases is a must
- Spring is optional but I strongly recommend. Spring is a big library but you can pick and choose the bits you like/need.
- Web frameworks the choice is really yours. From what I have tried (JSF/JSP/Wicket) Wicket is the easiest to get going with so you don't spend too much time frustrated with the getting the initial setup. JSP is awful, it's very easy to make a mess with it. JSF is powerful but heavy and probably more suited to very enterprisy projects than a first web app.
- Hibernate is optional but can make life easier simply because you can work with Java objects when you do DB queries/updates rather than writing tedious insert/update statements. Hibernate isn't the only tool like this but it's the one I've used most and does the job well. Just don't go too overboard with the "clever" hibernate features initially.
You could easily use Spring MVC instead of Wicket. That may be a perfectly good choice, I've not used Spring MVC myself so can't comment. I'm sure it will integrate well with spring stuff tho so that would certainly be a positive factor.
Do some more research if you're not sure, there's no end of people happy to give their opinion! But really you just have to dive in and try something.