Eccleston's 2005 series is a very nice intro, and since they didn't know if the revival would work, it's a complete line in and of itself without the later years overwrought bloat, very fun watch. Meat filled pumpkin to roll about your enclosure
the 9th doctor to the end of the 10th is only 5 seasons, 13 episodes a piece. And each season serves as a good "End point" if you only watch 1 season, or only go till end of season 2 or 3 its still a really satisfying ending.