Hello Romeda,
I guess you could say Adobe Illustrator and Adobe Photoshop are "brother" and "sister" programs. While Photoshop is a Raster based application (in that, as a paint type program it deals with pixels), Illustrator is a Vector based application and uses coordinates and such to define the image.

Illustrator is more than sufficient to produce the artwork you need as stated, BUT if price is a concern, you may want to look at other alternatives. There are programs like:

Macromedia Freehand (which is just as powerful as Illustrator)

Macromedia Firework (which is perfect for web work and log design)

Corel Draw Graphics Suite (sorry i have no experience with this, but i'm sure others have...)

Xara X (again, i have no experience with this other than the demo...)

Creature House EXPRESSION3 (there are a number of users in the 2D forum that use this app and swear by it!)

For more indepth and rowdy opinions stop by the VECTOR forum a post the question (or link back to this...), i'm sure they'll have a thing or two to say...

:)
retrocity