So I completed the Paladin Class campaign, earning my third relic slot on my artifact weapons as well as the first color of the "souped up" version of each appearance. My Truthguard is even bigger and glowier, and my Ashbringer looks really huge (though I really don't use it much, as the artifact system makes it tough to really maintain two specs - hopefully something that will improve as the expansion goes on.)
The class campaign is pretty good, though obviously if it's something you can complete in the first week of the expansion, I sure hope there's more coming. I get that designing quests and such for twelve different classes is always going to be very time-consuming, but I hope this isn't the end of real class-specific content.
Before I go into plot details, let's talk rewards. Obviously you get your upgraded artifact appearance (the first color variant - the others are unlocked through other means.) You also get a third relic slot, and this aspect I think makes completing the campaign a real must-do for any serious character (though it's hardly a real burden - you'll just need to do a few quests and champion missions.)
One unexpected but highly welcome reward is that for completing the campaign, you get the title that people have been addressing you with as an actual in-game title. So far I know that Paladins get Highlord, and I think we have Deathlord for DKs, potentially Slayer for Demon Hunters, Conjurer for Mages, Archdruid for Druids, probably Farseer for Shamans, Shadow for Rogues, I believe Cardinal for Priests, and the rest I'm not so sure about. Grandmaster for Monks - there's another.
You also get a massive chunk of order resources and a big boost to artifact power.
At this point I've also gotten my first rank of Artifact Knowledge, which currently increases the rate at which one gets artifact power by 25%. You also get a book of lore on your artifact weapons, and apparently as this gains more ranks, you gain more lore in addition to the mechanical advantage.
My understanding is that as the expansion goes on, they'll either make artifact knowledge quicker to research or each rank will provide a bigger bonus (or both.)
Ok, onto the specifics:
Ultimately, Paladins are on the hunt for Balnazzar - the Dreadlord who corrupted the Scarlet Crusade and who was responsible for Tirion Fordring's death. While searching for him on a Legion-broken world called Niskara, we learn of an attempt to invade Netherlight Temple - the Priest class hall. We also meet Lothraxion - a non-demonic Nathrezim who is a high-ranking officer in the Army of the Light. We free him from his prison and then make preparations for the defense.
Eventually, this leads to a battle at Netherlight Temple where we face down Balnazzar. Just as it looks like he's about to win, a gleaming white Naaru vessel arrives and Lothraxion comes to aid us, sent by Exarch Turalyon. We slay Balnazzar, scoring a great victory for the Light.
I'm curious to see if this is similar to the Priest campaign - given that we go to the Priest Class hall and defend their temple (which to be fair, is a pretty Paladin-y thing to do) I wonder if their campaign has a similar conclusion. Then again, I know that some other class campaigns send you to others' halls, so we'll see.