Help a newb with drawing basics

Ive started to design web pages. While Ive got to grips with basic layout and colours, I want to begin creating banners, logos and background images.

Ive started to use photos and just editing those changing effects and fades etc. But I really want to start getting into Graphic Design.

I don’t really know where to start really. I’ll admit im not the best drawer in the world, but i can sketch ideas ok. But how do i do this on th computer ? I cant really afford a tablet at the moment.

Say for example, i want to draw a cartoony cow, and then colour it and add effects. Where does it all start ? Should I use vectors ? Photoshop ?

Any help would be appreciated, thanks.