I'd recommend Illustrator. It's what people in the field are using. I've heard that Illustrator and Freehand are very close, although I've heard Freehand has had it's quirks and bugs. Like extra stuff will be placed in random spots rather than just all together. Also, Freehand has been able to integrate better with Flash, and I think that had a lot to do with the fact that Freehand and Flash were both done by Macromedia.
Now that Adobe bought out Macromedia, the Adobe CS3 should be better integrated with each other. So if you were to buy a CS3 version of Illustrator, it would probably be easier to integrate with Flash. Though when I took a Multimedia class in college, I don't remember having or hearing any problems with Illustrator and Flash.
You can also buy a tablet and actually draw into Illustrator. Usually the Wacom are the best: Wacom Products
For tutorials, I was going to list a bunch, but if you type in Illustrator tutorials into google, you'll get a huge list. I figured I could just let you pick and choose.
"I would feel more optimistic about a bright future for man if he spent less time proving
that he can outwit Nature and more time tasting her sweetness and respecting her seniority."
E. B. White (1899 - 1985)