Yet another premise that would have made more sense than what we got. Better yet: cut out the First Order, and have them be a more "regular" Imperial Remnant that signed a peace treaty not too long after Endor. They're not insane fanatics, and there's been peace ever since. Then both sides start accusing the other of attacking then without provocation, and it looks like there'll be another war...
Some shady crime cartel -- which wouldn't have to (limited to) the Hutts -- being behind it since they control the arms industry and are seeking to exploit such a conflict (both via profit, and due to organised crime getting easier in a chaotic situation) is an idea that fits perfectly with some of George Lucas's sequel ideas. The idea of large corporations (in this case the arms industry) being villains also calls back to the prequels, so it fits into the larger theme.
This plot can easily be combined with ideas we've discussed on this site before:
The New Republic and the Imperial Remnant both have trigger happy "radical" factions, and the crime syndicate is exploiting those sentiments to push the galaxy towards another war. The son of Han and Leia isn't a traitor who joined the Imperials, but a member of the fanatical anti-Imperial group in the New Republic. Finn is a moderate, "normal guy" stormtrooper in the Imperial Remnant.
In the end, the conspiracy is uncovered, the crme syndicate is defeated, the radical Neo-Imperials are brought down, and the radicals in the New Republic are either improsoned or they repent and change their views. The New Republic and the Imperial Remnant sign a more durable treaty, and their trade relations (et cetera) are normalised.
...Of course, Tim Zahn already wrote something very much lik this story back in 1999, for the original EU. It's a duology called The Hand of Thrawn.