The series has had it's ups and downs.
The first two doctors were in black/white and not many shows are easily available. I used to watch them on PBS when I grew up. All but the newbie die hards will say they move too slow... but that's where all the original long-running character creation came from.
Dr 3 (Jon Pertwee) was a favorite. He was SUCH a lovable curmudgeon! Great stories and good companions.
Dr 4 (Tom Baker) had a long stretch and many of the old timers really got into him. The iconic scarf is probably one of the best Who Props! And who can say anything against Lalla Ward... my favorite Romanadvoratrelundar.
Dr 5 (Peter Davison) was good, but the traveling companions left me flat
Dr 6-7 (we just won't talk about)
Dr 8 was only around for a movie so, nothing much to see there
Dr 9 (Chris Eccleston) was a bit of a jerk but the story lines were really good and fit that kind of Dr. Plus, he introduced Rose who was one of the better companions.
Dr 10 (David Tennant) is my daughter's favorite. The stories were really good and his quirky character fit the stories very well. The younger generation tends to like this doctor; he was an EXCEPTIONAL Doctor.
Dr 11 (Matt Smith) was way quirky and the plot lines got really twisted (in a wonderful way) but you cannot watch Steven Moffat written scripts passively. You need to pay full attention to what's going on... then after you get to the end of the series go back and watch the whole thing again. The arcs in the plot that are not even arcs that you can recognize at the time. The stories are BRILLIANT.
Dr 12 (Peter Capaldi) has been out for a few seasons... I kinda like some of the stories, but his character just annoys me. The only saving grace is Jenna Coleman's character.
John Hurt played the Dr for one episode which was very fun. Watch the other doctors before seeing this one.. it will make much more sense.
My suggestion is to start with David Tennant; work forward from there and then loop back to Jon Pertwee.
As you get deep into the Doctor, look at the backstory and some of the facts behind the camera. There's a lot of great documentaries out there about the start of Dr Who that include the original producers and Verity Ann Lambert's groundbreaking first female in a very male producer club; the call for "No BEMs" (Bug Eyed Monsters); also, some of the fun facts... like Tom Baker married Lalla Ward (his companion) and Peter Davison's real daughter Georgia Moffett married David Tennant after she stared in an episode titled "The Doctor's Daughter" (she was supposed to be a genetic merging of David Tennant's Dr.) ...a bit incestuous no matter how you look at it.
Have fun with the backstory and good luck on the mod!