SSO Graphics

i’m looking for something that creates high quality images (logo and small icons for webpages) and in the same time images are with reasonable size for fast loading. all i know it has to do something with vectors. what are some of the most famous products out there?

I’ve draw out my logo on paper, but I need software to draw it on my computer. Any suggestions on a good software to use?

I have a picture that I drew by hand, I wanted to color it with gimp but my drawing’s lines look really bad and I want to sharpen them and make them look darker, is there a step by step instruction on how to do them?