I agree with all of the posts so far. Good suggestions.
There are reasons why most graphics professionals shell out the money for Photoshop. This does not mean that it's the best graphics program -- just the best for them.
When you're working at web resolutions, you will see little or no advantage in using Photoshop. In fact, I could point to a couple other products that you'll probably be happier using.
That said, I have searched for a product that would allow me to stop paying for Photoshop for professional work. Suffice it to say I am still using Photoshop and will be for the forseeable future.
Photoshop becomes indespensible when working on high res (300 dpi or higher) 4-color press-ready artwork. RGB-only applications are great for just about anything else, but are pretty worthless with respect to color correction and high res work. A slight shift in hue matters in the work that I do, and most service providers charge for color correction. Just for that, Photoshop pays for itself after a couple months.
Photoshop's algorithms and features are better, but you won't notice that at screen resolutions. A 4-color full page ad can easily be in excess of 50 Mb in size, and I just haven't found any other app that manipulate files that big as quickly as Photoshop does.
If you are not working with these kinds of files, don't need to create press-ready EPS images, etc., then you'll be just fine in PaintShop Pro, Fireworks, Photoshop Elements, the GIMP, and other very good apps like these. Photshop does web graphics, but that's not primary reason why people buy it.
That whole "press ready" thing probalby sounds a bit snobby, but that's not what I'm trying to say. It's <em>not</em> a matter of "real" graphics work versus "amateur" graphics. It's a matter of the right tool for the job.
Photoshop does not equal professional, and
not-Photoshop does not equal not-professional.
That's my two cents. Someone may find that something I said was oversimplified, but I've already written too much and a more complete explanation would be well beyond the scope of your question.
Hope that helped, or at the very least didn't just muddy the waters. Good luck with your work!