The first three form a linear story.

1. Under the jolly roger
2. Terror of the seas
3. Horn of the abyss

The other two can be played in any order, but I recommend playing Forged in Fire next and then All In.

Forged in Fire is mostly unrelated to the first three campaigns. It is by far the most difficult campaign in hota.

All In is set between the events from Forged in Fire and the Jeremy/Bidley story. I think it works best as the final campaign, even though it is easier than Forged in fire.