Anyway, I don't want her to be a trap, or someone who dies every week, or any of that gimmicky stuff. I don't want her to be a story arc, I want her to be a companion, one who can stick around for a good long run and be a fully realized character rather than just a plot device.
Well, in fairness, Amy was essentially just a plot device in Season 5. The only reason The Doctor decided to keep her around was because of the crack in her wall. Once the cracks were sealed, though, she became his friend and, I think, the best companion that he has had since Rose (in terms of his relationship with her, not in terms of how much fans like her).
He was going to take Clara on as companion before he knew she was a plot device. Then she died. Now she is a mystery that he wants to solve. Once solved, assuming she's still alive, there's no reason she can't make the transformation from plot device to actual character.