As noted there are basically two campaign systems provided, which can be used on their own or in combination (and either can be used with or without progression systems).
The one I am going to take a look at today is the Campaign Story - This is basically a fairly open-ended and narrative campaign approach where we focus primarily on story beats.
I am going to play through 4 "rounds" of this. A round can have any number of tabletop battles. This might be a single battle (if you want a campaign with lots of events) or every 2-4 battles if you want more tabletop time.
In this case, I am going to be working with a campaign pitting Unity troopers trying to take out a moon base held by notorious pirates.
I will be taking the role of the Unity grunts and my campaign will follow a platoon or so of troops (say 4 squads and a walker for support). You dont have to follow a specific unit but thats the typical: Its more colourful if you do.
The opening battle is probably a direct assault: The Unity grunts drop from their shuttles and have to fight through a thin defensive line of pirates. You can use an option from the book or just concoct your own. We are starting out easy, so I might be up against half my number of pirates so we don't end up gaming out the opening to Saving Private Ryan.
After that I roll for the first story event and it is Side story. A secondary story takes place during the campaign. Having a think I decide that before the troopers storm in, there was actually a schism in the pirate ranks and a firefight had broken out. In that case my next scenario will be the two pirate factions slugging it out over who gets to be in charge.
I could do multiple battles here but I decide to just do the one and then generate another event.
The second event then is Unconventional Operation. One side carries out a special operations mission of some sort. I could pick randomly (I like assigning a 1-2 / 3-6 chance to the two sides) but it seems obvious the grunts are going to be doing this. I come up with a quick scenario where they have to raid and blow up the pirates shuttles so they can't escape.
I want a bit more table time this round, so I also play out a standard firefight where my platoon is getting stuck in with the pirates on the barricades. The special operation will be a new unit that I name but won't otherwise follow.
Event 3 is a Critical Strike. This indicates an assault on a priority target of some sort. Seems similar to the prior event but the stakes here are higher. If my grunts won their mission, we are probably in position to knock out the defense networks of the base, allowing the rest of the army to show up. But I decide actually lets turn it around: The pirates are going to try to push through and recapture a big defense cannon to shoot our shuttles out of the sky. That should make for a fun and tense scenario.
Luckily they fail and I think by now the pirates are probably on their last legs. I am going to interpret the last event with that in mind. I roll a New Character. This is what it sounds like: A new character is introduced to the story, typically in the players unit. I think this campaign is probably gonna come to a close here but lets leave a hook for later: A mysterious Unity field agent shows up and commandeers my platoon to secure a strange cargo crate, under strict instructions that they are not to be opened.
I am now set for the final mission of the campaign and with a good hook to set up a new campaign.
I hope this helps show how the campaign story can unfold. Each result in this example was rolled randomly. The results in the book all come with both suggested player effects AND have a tie-in to the operational campaign rules if you use those but more on that in the future.