what do you mean by hyperlink icons? Are you talking about graphics that you click on to follow a hyperlink?
If that is what your talking about, adode photoshop or gimp or any number of image creation manipulation programs are available, but all the powerful ones to my knowledge require some level of expertise to use efficiently and effectively.
Hyperlinks don't necessarily have to be images, they can also be text. But, if images are what you need then mat_bastians' suggestions are are on the mark. There are many, many image creation applications out there, with Photoshop pretty much being the best of the best.
Photoshop 7 is the latest version, but you will get trial versions of this and free copies of older versions (check out some design mag CD's) easily enough. Try out a few different apps and see which one does what you need. Many people think Fireworks is the bee's knee's (I say that out of fairness - I'm a PS man all the way!).
You can also get lots of free icons on the web - but for uniqueness and individuality, you'll probably want to make your own!
If you're looking for affordable image software, Paint Shop Pro always gets raves... GIMP is open source, but I haven't heard much about the learning curve on it... Fireworks is getting more expensive, but I've heard it's fantastic for web graphics...
I wouldn't recommend PhotoShop to a beginner who was only interested in doing web graphics though, it's really expensive, and would be rather like using heavy field artillery to go duck hunting. ;)
If you want to get into print design as well as web design, go ahead and invest in PhotoShop, but otherwise, you could find a cheaper more newbie-friendly piece of software, IMO.