This question delights my nerd gland, since I endeavoured to watch all 695 episodes of the classic Who. I started in 2008. The pace and writing of the new series are very different from "classic" Doctor Who.
Because there are so few landmarks of linearity from one Doctor to the next, I think it's safe to start with whichever Doctor you like best. Since I have good memories of watching Tom Baker episodes when I was a boy, I started with Robot, the first Baker serial. I didn't want to have to wait ages and ages to get to the Baker stuff, and I also didn't want to end on the sour notes of McCoy and McGann. Starting with Baker and then looping back to Hartnell also meant that I would conclude with the transition from Pertwee to Baker, which was perfect.
I'm now halfway through the Troughton years (Doctor #2). It's pretty arduous slogging through the lost episodes, but you get used to it. I took a break from Who for a while and finished Blake's 7.
My personal ranking:
1. Tom Baker (a Doctor who's fun, has presence, conveys brilliance, and shines despite the show's meager budget)
2. Hartnell (the most dignified and patient doctor; the gentleman scientist)
3. Pertwee (grey pompadour ftw. He might climb this list someday.)
4. Davison (hypertensive fun. Cricketing whites 24/7.)
5. Troughton (too bad many of his episodes are boring)
6. Colin Baker (a bit angry and dysfunctional)
7. McGann (what a wimp!)
8. McCoy (utter retardation)