You have two main options:
1. Flash. Costs money (quite a lot in fact). Flash does proper animation - people actually make cartoons for TV with it. Flash can be used at many levels, from simple drag-and-drop animation tool to full-scale programming environment. Your HTML and CSS experience will be no use in Flash, but if you know Javascript, you'll find a lot of Flash Actionsctipt understandable.
2. Javascript. Free. Perfectly adequate for making interface elements (like menus) move. Rather than write Javascript from scratch, the best place to start nowadays is with a Javascript framework such as prototype, jQuery or MooTools. Using one of these libraries will save untold hours of frustration.
Ignore Silverlight and Java for now - neither is widely used for the kind of thing you're asking about.
Having said all that, think carefully about what you're trying to achieve. Animation is not something that will appeal to everyone; a lot of people just want to read a web page, not watch unicorns prancing across it. And there are accessibility issues when using Flash to provide navigation on a site.