I work as a freelance illustrator and animator and the two that I would recommend is certainly Illustrator and Photoshop. From my experience dealing and working at design studios, very few use Corel Draw if at all since Adobe (company that makes Illustrator and Photoshop) is the standard software package that people use.
Illustrator is used specifically for "illustrating things" and photoshop is suited for photo manipulation and adding effects. You will learn that they go hand in hand as many illustrators export their work from Illustrator and add special effects in photoshop.
For example, here is a good reference to the things that can be achieved by using the two programs in regards to what you would be looking for....
http://art-dept.com/illustration/index.html
Look at the work of Miles Donovan - You can see unique patterns and photo images manipulated in his work, this would be done in photoshop.
The work of Bo Lundberg (one of my personal favs) is all done using Illustrator as you have very clean, vector style graphics.
I hope that helps
