Here is a few things for you:
The war is never seen on TV. I happens off screen during "The War Doctors" time. The war doctor is only seen in one episode. Considering how much is devoted to this pivotal moment, there's actually not much on it.
Each person love a certain doctor. Colin Baker is deemed the worst because he was made to be not lovable - a bit of a jerk which is totally different portrayal of most doctors. Also arrogant. He's very different.
Me personally its Tom Baker, the absent-minded yet somehow quick witted and Eccleston the Nihilist - I love how he is so gleeful when he's just about to die. And he didn't wear a suit! Fantastic! He plays the whole grief over what he's done better than the other two. Tennant plays angry awesomely though.
I'd say 2005 is a good start. Starting right at the beginning involved "special effects" like cardboard creatures and actors run into and pushing over sets. Its pretty awful but fascinating if you want to see what TV shows were like in the beginning