Someone else can chime in here but without actually taking a ‘good’ solenoid and testing it, I’m going to say at least a ¼ inch of travel and 3/8” sounds better.
IF I recall correctly, about 3/8" sounds right.
Regards, JLB
It should be added that (at least the ones on which I have worked) the pall out of the solenoid is spring-loaded so that it can "spring" into the next available notch when rotating.