I agree that the positions you mention are where we need to shop first, but not for cover or back up, for improvement. As for the suggested names to go for, have you got a wish for us to become Bournemouth, Southampton, Burnley or any other mid- to low table team? Which of those players would be a starter for a team pushing for titles? None.
We need more ambition than that. The reason we are where we are isn't only because we lack squad depth, it's mostly because we lack pure quality. If we want out of mediocracy we need to get the quality first, and then add the depth (if needed).