I was guessing a military ship as well, but you may well be right that it would not be the best for starting a colony. I don't think any of the choices are really ideal, but I would guess that's really the best shot (or some combination of the choices? Maybe a cargo ship contacted some smaller civilian cruisers, or a group of smaller military or commercial ships banded together and decided it was their best bet). As far as Iceland goes, I think they would need to look at it more for its military importance than as a reasonable place to relocate civilians. It's small, even compared to Svalbard, and I think that the radio station and airstrip would probably be the most valuable things there.
Speaking of which, do we know if Iceland had military planes at year 0 in SSSS? I don't think it maintains its own air force, but there is a NATO presence there and I know that Reykjavik has its own airport. I feel like this would be an important detail, because if, for some reason, Iceland had no planes, I would think obtaining and maintaining them would be a first priority (especially given that this would be the only easy way to travel without being harassed by trolls).
Also, Jan Mayen actually *might* survive without a ship, as it maintains a research staff of up to 18 every winter, and has supplies to support at least that many for about a year. But any society of 18 would be hard-pressed to survive and repopulate for 90 years.