It really depends on what you are trying to do.
Personally, I would begin with illustrator. It allows you to draw lines that you can fill in to create shapes and layouts.
Photoshop is the other one that you should look into. It deals in image pixels directly. This is more of a painting program. You draw with layers of color that stack to form the final image.
Either way, both of these programs produce pictures. I would recommend working in a bit of both: use illustrator to layout you initial idea, then draw it out proper with photoshop.
Most of the other Adobe apps are irrlelevant to what you are doing (z.b. Soundbooth/Premiere are for sound/video).