You can use Photoshop, however, Photoshop's main strength are images. I suggest you try working on a software that mainly works with vectors. For example, Freehand, Illustrator (can work both images and vectors), etc.
Freehand would be the best for vector images (Photoshop is OKAY, if you do not have a program specifically for vector graphics)
Good suggestion. IMHO, I would go for corel because of its easy to use productivity. I've tried it before and learned it quickly.
I may be missing something, but how exactly would you save a photoshop file so that it's vector art? I know you can use vector tools in PS, but if you can save a file out of PS as strictly vector, I'd like to see it done. PS is a raster-based (pixel-based) program, as far as I know. .eps files saved from PS are not vector .eps files, contrary to popular belief.
adobe illustrator is good in vectorizing images ndesign-studio.com/resources/tutorials - here are some tutorials