Rainmin12 is correct, what matters is what months you had HDHP coverage. Enter Self or Family for any month in which you had HDHP coverage, and None for any other. Note that caverage is determined by the first day of the month - i.e., if you started HDHP coverage on the second day of the month, then you had no coverage for the month as far as the IRS is concerned about your HSA.
While the information on what policy(s) you had is on the various 1095 forms, you may not recognize it. Contact your employer's benefits person to confirm which months you had HDHP coverage (or call the insurance company).