I don't think there should really be a campaign, but maybe more of just written books in generated structures like villages or strongholds that give you some background.
I have an idea that builds on my idea. There should be certain items that can only be obtained from quests. One of these is something I came up with which is the venomsaber. It is a sword that causes the poison effect.It should be equal in damage to a regular stone sword but have the durability of more than a diamond sword. The poison effect should be an enchantment, but no sword you can enchant should be as good as this venomsaber.
I like to think minecraft is just an island. Steve is on a boat during a thunderstorm when it wrecks. He gets knocked out of the boat during the process. Steve wakes up on the shore whilst it being night time so he travel a little further until he grows tired and falls asleep. Where you spawn is where you wake up from the sleep. The zombies are humans that were transformed from the slime of the slime aliens. There was only one group of settlers that came here hundreds of year ago when they discovered the slimes (which they shouldn't have touched!) Villagers are just the cousin species of humans sort of like lions toward ocelots. But, since they have such a small IQ level they didn't achieve procreating many times. Not to mention that they are all of the same gender and they immediately give birth after procreation just like everything else on this mysterious island. Oh and back to the point, the villagers have books in their library that are from past settlers that lived there. They teach Steve things like enchanting,the island's special type of self powering electricity named in the book as "Redstone", How to get to hell, the research on all the creatures on the island, and as much as they know about the end although they never got their. Steve is the longest surviving players ever.
Hmm I'm impartial about that.