If you're taking it seriously, definitely go for Adobe Illustrator. You don't 'need' a tablet, but if you want to buy one also, they aren't that expensive anyway.
I learned to draw with the pencil tool in Adobe Illustrator using a mouse and can create detailed vector illustrations with a mouse, I got so used to it, now when I try to get used to a tablet I cannot at all, and keep giving in. The tablet makes my hand cramp and it's a massive learning curve trying to control it, as it's become so comfortable with the mouse.
Amanda