Graphic design or web site design? For the former, I'd say the Adobe product line is still the most feature-rich, but maybe you don't need all the bells and whistles that come with a ludicrous price tag? There are some good alternatives. Sketch 2 (OS X) is very, very good and I use it more than Photoshop for graphic design tasks such as creating icons and the like and it costs merely a fraction of PS. You could also check the Trial version for Adobe Photoshop Elements, a trimmed-down, lightweight version of Photoshop. And there are others. But, like I said (and has been said by others already), it really depends on what you'd like to do with it. If you do more line art, then a vector program is the more apt choice. If you do more artistic stuff, then Photoshop or Corel Painter are better suited.
For web design itself, you really need a good text editor like Sublime Text 2 or Notepad++ as you'll be using that about 90% of the time as a web designer.
Eventually, you need to define what you need and then do a search on the net and try out the various options available and see what you like best.