When to shoot 24p? 24p Advanced? 30p? 60i?

The general rule is to shoot 24p Advanced if you want to extract the original 24 frames/second for a 24fps edit or film-out. Shoot 24p Standard if you are going to stay on video and edit at 30 frames/seconds (60 fields/second, i.e., plain ol' video at NTSC frame rates), without extracting the original 24 frames into a 24fps timeline. In more detail:

Shoot 24p Advanced for:

Shoot 24p Standard for:

Shoot 30p for:

Shoot 60i for: