Some more packages to add to Chl's suggestion of Processing for creating interactive visualisations. All these are javascript-based and can run in a browser, so can be used for publishing as well as for your own analysis:
- D3.js is the successor to Protovis. It's more powerful in that you have more control over the objects created (they're proper DOM objects, i.e. you have full control over them using javascript), but some prefer Protovis for simplicity. Good technical D3 vs Protovis discussion here.
- Raphael.js is a good option for highly customised mass-market web interactivity since it's both future proof (no flash) and works on browsers as old as IE6 (the only thing it doesn't work on that I know of is old versions of the Android browser). Like D3, everything is a targetable DOM object and it has good built api controls for animation and interactivity. It offers nothing out of the box that is specific to visualisation: it's a very powerful and flexible blank slate, a great choice for designing custom visualisations but not for your own initial exploratory analysis. Get acquainted with your data first.
- gRaphael.js is standard charts (bar, line, etc) for Raphael. It's basic but works and can be built upon - might be a useful ingredient if you are building your own suite.
Regarding your other question about learning, for general principles, Information Dashboard Design deserves a mention, if what you want is to make an array of general purpose interactive standard tools for your data.
Interactive visualisations are on the line between stats and interactivity design: so books on that may be of use. I don't have any personal experience of any of the many interaction design textbooks, but I am a big fan of Universal Principles of Design. It might be overkill for your needs, but consider looking down the Usability column in its excellent Categorical Contents page and reading the chapters listed (progressive disclosure, signal to noise, etc).
Also, for anyone new to programming, Programming Interactivity is a good place to start for beefing up technical skills (it also includes a hefty chapter on Processing).
But for knowing what works and what is possible, you can't beat learning by doing, and a good kick-start could be to consider trailing and analysing the big-name big-price-tag general purpose interactive visualisation packages like tableau and jmp, and think about why their features are designed the way they are.