Adobe Photoshop at the very least. - $649 for a single license
Some people like Fireworks better for specifically web graphics, but Photoshop can do everything and more. I use both. Get Fireworks for: $299
Illustrator if you will be doing graphics for print & web (like a logo - it would be silly to make a logo in photoshop and then need to do it over later if you are making business cards or brochures). Illustrator - $499
Some people prefer Freehand to Illustrator, but I think Illustrator is more powerful: $399
Flash - if you're going to be any sort of web animation, interactivity, banners, on-the-screen web ad popups, or more complex stuff, you'll need this. If your web design department will be doing work for outside clients (I don't know if you run a studio, or what), then you'll need Flash. It's something you should have, because you will find you will use it. Only get Flash Professional! Flash Pro: $699
Or get the whole shebang in one awesome bundle: The Adobe Web Bundle for $1899 - Photoshop, Illustrator, InDesign, GoLive, Acrobat Professional, Adobe Stock Photos, Dreamweaver, Flash Professional, Fireworks, Contribute, Flash Paper - literally ever piece of software you'd ever need to do web graphics!
Acrobat and Contribute are great, though not 100% necessary. If you're doing web stuff, you'll also need Dreamweaver!! Stand-alone Dreamweaver costs: $399
So, compare the bare minimum of: Photoshop, Flash, Dreamweaver: $1750, or get absolutely everything you'd ever need for $1900!