I'm a bit confused by the large family of Adobe products and packages. I'm looking for a product to do web related graphics and animations. I want a product that'll make great web graphics, similar to the ones you see as a header for a blog. In addition, I want to make other types of graphics that may appear simple at the moment, but visuals that will improve as I get better with the program, so view these examples as starting points.
Flash is probably the most appropriate for your type of objectives.