Yesterday I got a new contract to design an unique logo for a new internet company from Germany. They want it simple and unique.
To get some info into this forum, I thought I share my experience with you:
For vector based graphics, Adobe Illustrator is a nice piece of software. It has tools for all kind of shapes like circles, boxes, triangles, etc. It is not for creating web graphics, rather for creating print material.
But if you want to create a logo, it has some advantages: In pixel-drawing you tend to bloat a graphic and dither the whole thing. Not with vector based graphic programs.
Logos need to be simple and clear. With Illustrator you got the perfect design tool!