I would definitely create buttons or icons in Illustrator (but you still don't have to do that), and do a lot of everything else in Photoshop. You can try Fireworks and see if it's your cup of tea, but Photoshop definitely isn't going anywhere as far as standard practice for awhile, at least from what I've seen. I've worked with startups all over the country and top web development firms and still all I see is Photoshop/Illustrator.
Not to say Fireworks is bad or you shouldn't use it, but take it as a grain of salt and see what works best for you. It never hurts to learn new things.
Ctrl/Cmd+click with Photoshop move tool automatically selects the layer that is under your mouse cursor raster. Not 100% Illustrator-style but less BS than selecting from lists.
Good web design begins much earlier than Photoshop/Fireworks, and doesn't even move to the graphics/proof stage until you've made dozens of decisions beforehand that will influence your design (think business goals, marketing messaging, platform, audience etc.) HTML/CSS is almost one of the last steps in a complete web project.