Hmm... too many posts to quote anyone directly, but, on the subject of companions it occurs to me that different incarnations of the Doctor have different attitudes towards them.

One and Three both start off as thinking that they don't need them (except for Susan at the start, different because she is a relative) but ultimately come to grudgingly like and respect them - best exemplified by One's attitude to Ian and Barbara who start off as unwanted annoyances and become boon companions, and Three with Jo, who follows much the same arc (a good poignant moment comes at the end of The Green Death when the Doctor quietly leaves Jo's engagement party. I'd also perhaps put Nine in this category.

Two and Five seem to like having a small gang of companions along to ejoy the ride, both are of the more easy-going incarnations. Eleven, to a degree also follows this pattern.

Four, Six and Ten seem more prone to bring someone whose job it is to be impressed by them, although with the earlier Doctors the companions, although often in awe of the Doctor, are also not afraid to puncture his pomposity. There is also a great meeting of equals with the Romanas, also partly due to the real-life fact that the actresses could hold their own against Tom Baker's own pomposity.

Seven and Eleven, on the other hand, seem to pick people because there is something interesting and wierd about them - hard to generalize with Seven too much as there's only really Ace to go on (Mel being a holdover from Six); but Ace's background with Gabriel Chase (and the fact that she is in the wrong time when he meets her), the Crack in Time in Amy's bedroom and now Clara as the Girl Who Lived Ttwice ... as much problems to be solved as they are people.