I think this is a pretty straight forward question - My hard drive is failing (spinning/rotating platter hard drive).
Which of the following options is the safest way to back up the hard drive when some files are more important to recover than others?
Turn on the computer, load the failing startup disk, and back it up with Time Machine
Turn on the computer, load a recovery partition from an external drive, and use disk utility to "restore" the whole drive to another storage device
Use target disk mode and clone important files to another another mac
Is there a safer or better option? What's the right procedure?