I have been asked this many times, and simply, there is no right or wrong answer..

Some people believe Adobe Photoshop is better then Macromedia Fireworks, some may be opposite, and some people may prefer something completely different.

If you are a new Graphics Designer, or a basic Graphics Designer, i would suggest you use the free piece of software called Paint.NET.
It’s simple, and it’s free, and it does whats needed/wanted.
Link – Paint.NET

If you feel you are ready to take something a little more, confusing, or challenging, and want better results, go to Macromedia Fireworks. It’s quite easy to use, and you get great results from it. There is only about 2 problems. There are a lot of features and tools, so it can get quite confusing, and it’s not free, so before you buy it, try out the trial version.
Link – Macromedia

Now, for more advanced users, or those who like a lot of tools and features, i suggest Adobe Photoshop.
It’s powerful, much like Macromedia Fireworks, and gives you the same quality.
Link – Adobe