For my players I’m thinking of having an open-ended campaign. Where we make up the missions as we go but with goals they are trying to achieve for their house.
Eliminate 1 or both of your rival houses by total annihilation or destroying their house status by scandal, intrigue or espionage.
Raise your house status from minor to major by securing a spice (or other commodity) contracts.
Just spitballing ideas wondering if anyone else has some Interesting goals that would be your houses objectives?
Generally speaking, one would expect a house to seek to expand its power and status. From minor house to major, then to great house, and at that point one might perhaps have imperial ambitions.
That said, some houses are definitively more content in their lot, perhaps seeing the throne too much trouble, figure these houses are more likely to hold status quo, and thus are perhaps more likely allied to the throne than working against it. Or otherwise are just interested in survival more than anything else.
Seeking power is not necessarily tied to other values: both the Atreides and Harkonnen are doing this, despite their different ethics.
So, goals. Figure out who you are, and who are your rivals. Figure out what is your long term goal. Figure out how your rivals impact your long term goals and this gives you a short term goal, which is most likely about reducing a rival’s power and/or increasing your own.
Methods probably depend on values and one’s specialties. A moral house is more likely to seek alliances via trade, marriage ties, service to the throne (or other houses above them). An intrigue focused house might seek to disrupt their rivals alliances.
Figure interesting goal depends heavily on many things. Some things to consider:
A player house most likely interested in playing their strengths, and less interested in things they’re not so good at. But a rival will attack their weak point, and trying to shore up their defenses in that area could be an interesting adventure.
Use your strengths to gain help/allies/vassals to shore up your weaknesses.
I would second the need for a rival. It doesn’t have to be a full on Kanly type affair, ala Atreides/Harkonnen, but even just a business rivalry can lead to all sorts of shenanigans.
Another thing to consider might be the relationships with the non-Houses. the Bene Gesserit, Spacing Guild and Bene Tleilaxu.
I think one of the other players on these boards had a long term plan which involved being able to surreptitiously bypass the Guild travel monopoly.
There is also expanding your domains, either by taking over someone else’s or developing virgin territory (either a new planet or creating something new in space or on a moon)
At the moment my players are focussed on internal divisions within their House. Depending on where your players are in the House manipulating the succession could play into matters as a goal.
I remember a Dune Board Game where players had secret house/faction goal