You don't actually need any! TextMate or E-Texteditor and a decent browser (plus a few free tools), or (for a complete environment) Coda or Coda alternatives. But Dreamweaver and Photoshop are a good foundation; possibly Flash unless you want to go HTML5 with your media delivery etc. Depends on whether you hand-code or want a visual environment, or a bit of both. You'll probably also want to get a grip on JQuery or a similar Javascript library.
Just for graphics, Photoshop Elements will do - Photoshop is overkill, as is the GIMP - unless you're using Flash for complex interactive stuff, you only need to generate jpg, gif (animated or not) and png files. Or something free like Seashore (OS X) or alternatives. As for Adobe products, Fireworks is the one. If you want to generate original graphics programatically, try Nodebox (Python), ContextFree (C-ish) or Processing (Java-ish).
Then there's the wonderful Raphaël Javascript library, and various html canvas examples...