Bit of a lack of context! Although I see from other threads that you use Dreamweaver, so Adobe products and price-points are probably not completely unfamiliar to you.
Proper in-depth graphics work first: Illustrator (excellent but very expensive) or Draw (cheaper; almost as good).
Cheap/free options for graphics: Inkscape (open source, but probably not as capable and it's a bit harder to learn) or Xara Photo and Graphic Designer 6 (overlooked but quite effective, well featured, and it's good value).
Serious photo editing: Photoshop (obviously)
Mid-range photo editing: PSP (yes, some minor functions could use an overhaul now, but it's mostly very effective, it's very cheap, and it's better specified than Elements) or GIMP (free, pretty effective though a bit quirky, and the manual is quite good which is unusual for open-source software)
Each of the last three can be used up to a point (to varying degrees) for some graphics work, though it can be harder to achieve what you want, depending on what you are trying to do. Photoshop is the best 'single-app-multi-task' choice of the three.
I use Illustrator, because that's how I make a living, and PSP for photo editing (which suits me just fine for the little that DxO Optics can't do). I'm not too keen on Inkscape, but it has potential. The Xara option is pretty neat for the price. All of the above is just one guy's opinion based on experience.