I know this will appear profoundly odd to you, but Amy is actually the one companion who makes me feel like it could be me there. The Doctor took her with him because he realised, or had a suspicion, about what happened to her and her family - but there’s no need to see this in a literal manner of “you have to have a crack in your wall to make the Doctor travel with you”. A lot of Amy’s character and story works in metaphors and for me that’s one of those things.
Because, really, he saw someone who was strangely out of place. A big house, a small girl. Damaged even, a life being devoured, pieces being taken she didn’t know she was missing. Grieving losses she couldn’t remember. She can be brave, she can fall on her feet, but she’s still misunderstood, still afraid of being abandoned, still scared too trust. She’s the most intrinsically flawed of all the companions, because she can’t not be.
He didn’t “take the best”. He took the most lost.
And maybe that’s a little messed up, but that is way closer to me than all other companions combined.
I’m really sorry if it makes you feel sad that you can’t find yourself in this, but you really need to understand that what you should feel like is incredibly grateful that another companion can do that for you. And grant me Amy Pond.
(And grant others Clara Oswald, who actually is an ordinary girl and whose echo the Doctor offered to take travelling long before he realised her connection to the girl in the Dalek Asylum.)