I use Illustrator and Fireworks. I use photoshop for some special effects but try and stick with vectors as long as i can until the gif/jpg stage so as i can transform them easily.
A lot of the most frequently used special effects in PS can be used in illustrator now in vector format which is handy like drop shadows etc. PS was never really built to make graphics, just to manipulate photographs but it serves the purpose to some extent. you might use it for blending a photo into a gradient for a banner and things like that but you can also do this in FW.
If you want to learn how to make graphics for web - get Fireworks and/or Illustrator, it'll make the job a lot easier and Fireworks has the best engine of the three for compressing images for the web. you'll notice the difference. The three all work together though.