If we only need to graphically authorize a user,
view a few tables representation (from database),
ability to change data in the database visually
what tools to use to write such a web application that will run on Tomcat?
What framework allows to do that in the most straightforward, easy-to-manage and elegant way?
There are so many elegant web frameworks available to choose from...
A JSF solution is a one suggested by the Java EE standard - if you select JSF you'll have to be more verbose in the code, but you'll have the assistance of tools such as the Visual JSF designer in NetBeans. Using JSF2 is a much better idea, IMO.
I personally recommend you to have a look at Wicket - it's a great Java web framework, centered around ideas such as ellegance, simplicity and usability.
There are many more great frameworks out there, but this is a start.
I would look at Spring Roo as the framework for building your app. It will allow you quick construction of most of the features you are looking for in several minutes. (or so they claim)