Turlough was one of my favourites. I’m not sure why especially, except that he brought the snark better than anyone. Tegan would complain and shout a lot, but Turlough got to be witty and elegant in his resistance to the Doctor’s particular brand of virtue and heroism.
“What is it about Earth people that makes them think a futile gesture is a noble one?”
There’s a popular idea that classic Doctor Who companions always start out with pots of characterisation and then gradually descend into bland screaming girls until they are finally written out at the request of the actor. I’m not sure that’s entirely true for any companion at all – it is true that many get stronger scripts to start with than later, but it’s rarely such a linear progression as fans (and perhaps the actors) tend to believe. Sarah Jane’s feminism waxes and wanes rather than sliding in a downward spiral, and the same is true for Nyssa’s scientific know-how, Jo’s spy skills, and so on.
It is rare for extra backstory to develop after a companion’s first appearance – though it did happen to some extent with Ace, and with Tegan. Many companions started out with almost no backstory and… never got any more.