You could simply work in photo shop if it's full color, having shading and gradients.
Make adjustments till you are satisfied, then do your separations.
If it's line art, or simple multi color with no shading or gradients:
What I do with hand drawings that are simply line art is take them in to photoshop and adjust levels and contrast to get the darkest/cleanest lines possible...
Then, work the MEDIAN FILTER to smooth any jagged or funky lines.
Then, take it into Illustrator and LIVE TRACE it.
(If line art, use Black and White Logo - If multi color, use color image, then use the number of colors: ie, 4-5-6-8-10 whatever)
Keep in mind that if it is very busy, Illustrator is going to smash on your computer tracing all the colors to paths.
That is why I won't even attempt shaded or gradient stuff in Illustrator.
This will give you a vector image.
Then you can go from there and make any necessary tweaks.
Bottom line, they both have their benefits, and both have their downfalls....
BUT... I'm no guru with Photoshop or Illustrator. I do well enough for myself and the work I do.
I know there are some guys that are absolute Illustrator gurus that are sick fast with doing it all by hand drawing/tracing over the existing art with paths from scratch. Especially with a tablet.
But, if you have Photoshop and Illustrator, you could give these methods a shot and see how it pans out for u.