How do focal length and distance to subject affect depth of field?

I understand the closer you are to the subject and the greater the focal length, the lower the depth of field will be. However, how do these compare with each other?
i.e. if I want the maximum depth of field should I zoom out and go closer to the subject or stand further away and zoom in?

Stand further away and zoom in

For a larger depth of field you want a larger aperture which you can’t get if you’re too close.