for starters you must for new who!
so doctor nine and so on...

but is 6 season now and 3 doctors?

i think you can start with the last two episodes of season one and then in season two with the Ten doctor (my personal favorite! ;) he is passionate and he is really in conflict with his guilt, with his love to humans (some of them in particular as romantic love and real friendship), and where he can push and he can change in human lives in order to save them.

season 2,3 4 are of David Tennant the ten doctor and 3 companions: Rose (who came from nine) Martha, Donna(my fav.) and the better bad guy ever The Master!

season 5 and 6 are of the eleven doctor Matt Smith and his companions: Amy pond, Rory, and the mysterious know too much about the future and i'm here and then not River Song.
11 is more playful, but he is more drastic than ten when he take a decision, he has no conflict, guilt yes, conflict no and he hides this in goofiness that is almost cute

the difference between doctors is that his personality is different and he is changing constantly in his approach at his loneliness, at his power over good and evil, his guilt, and life.

so I'm not sure ;D

but they are really fast to watch and if you don't like one you go the the next and if something is lost to you, ask me anything!