The Doctor only travels with the best. He finds them, or they find him, or they run into one another while he's saving the world or eating chips, and there you are. Off we go; into time and space!
And travelling with the Doctor – well, it's not like being with anyone else. There're definitely no taxes or mortgages or groceries to worry about. It's all aliens and stars and laughing and running and saving the world (or worlds, as the case may be). Mostly laughing and running, honestly; there's an awful lot of running involved.
That's something he looks for, one must suppose: the ability to run, and to laugh – at yourself, a lot of the time – and the ability to love and care and think and ask questions. These are the things he looks for, surely, as well as the ability to go without blinking …
But above all else, the Doctor looks for that something in your smile, your laugh, your tears, the way your hand fits in his. He looks for that shine, that glow, which marks every one of his companions.
Because the Doctor only travels with the best. And they are Golden.
Inspired by Lozzeh13 on YouTube – specifically, the tribute to Ten and his companions, set to "We Are Golden" by Mika. If you haven't seen it, you should; it's brilliant. Plus, the song is exceedingly catchy.