At Studio Pigeon our designers tend to draw characters or other assets on paper first, then scan and work with scanned ones in Illustrator or Photoshop using Wacoms. In my opinion the fastest way is to use digital tablet and draw directly in PS or AI, but as long as I observe my collegues, drawing on paper first gives nicer results (I don't know why :P). As it comes to tablets, check Wacom's Inkling to draw on paper and have Illustrator paths created that way ;) Also, heavier solution is Wacom Cintiq, check that one too :)
Hope this helps!
Blazej