Adobe programs are a bit expensive - I don't know where you live, but they are half price in the US in respect to what I pay in Denmark - so that would be the place to live. Try out GIMP and Inkscape first - they are both free.

Very short Photoshop is for handling images and painting - Illustrator is for drawing/Illustrating ... however over the years they have gotten nearer to one another, and you can of course import files back and forth. Especially in the newer photoshops you can add Illustrator items as smart objects so they don't pixelate when you scale them up (or down and back up).
Try visiting Adobes homepage and take a look at their product descriptions and check out the videos of the programs - you'll get a lot from those - also check out YouTube for beginners tutorials - they will also show you what the programs can do.

good luck