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There's definitely no right answer as to when to do main quest, side quest or exploration. It is important to understand that the game expect you to do some of the side quest and bounties, either for experience, money or materials.
1. Main Quest (Odyssey Section of the Quest Tab). Well obviously you want to do this. The main quest will take you to most regions, but will not have you explore the entire map on it's own, and will very rarely require you to come back to a previous region. So when the main story sends you to another region, I would suggest finishing what you have in that region before moving on, that doesn't mean doing everything, but what you plan on doing anyways at some point.
2. Side Quest (World and Characters Section of the Quest Tab). These are the Gold on Black icons on the world map. I highly recommend these, first most of them are fun, and can be pretty long taking you to different region and some have good rewards. They are pretty good XP also.
3. Bounties and Contracts (Bounties and Contracts Section of the Quest Tab). These are picked up on the bounty board, or are Silver on Black icon on the world map. These are generic quest with no real narrative to them. I would suggest picking all that you find, but not go out of your way to finish them. Don't be afraid to let them expire if they are not in your way. I say pick all of them up because for the most part they be completed as you do other stuff. It's decent xp, money and materials. Probably the safest thing to ignore. The contracts are long stuff like kill 15 leaders, again this is something you'll complete over weeks as you just play the game...there's no point in not picking them up. You just don't have to actively work on them if you don't want to.
4. Exploration. This I would definitely recommend doing. Explore all POI on the map. There's a few reason for this.
First is the Ancient Tablets, these are required to upgrade your ship and can only be obtained in random POI across the map. You end up with more than needed, so it's not too bad if you miss a few, or if you don't care at all for Sea Battles, although some are required for the story.
The second things is Tombs, these always have Ability points in them, and well more ability points is always good.
The third reason is that most Cultist are not tied to the main story. They are NPC that you can find in Forts, Region Leaders, and some are found on ships in the sea. You can kill them even if you don't know they are cultist members, this is actually how I killed most of them, if you don't do all the POI. You'll eventually have to return to these regions when you discover who they are, so you can kill them.
The fourth reason and I forgot what it's called, but it's those little quest thing that give you a clue to go find something. A lot if not all of these reward with Engravings so they can be useful. You get plenty of engraving even without doing these though, so they are optional.
The last reason is again xp, materials, and gear.
As for actively hunting Cultist, I wouldn't bother too much on this. First a lot of them are high level so you will always be limited by your level. If you do all the POI on a map, you will end up killing most of them by accident.
The bottom line, do what you enjoy. The more you do though, the more flexibility it will give you. More legendary weapons and sets and the money/mats required to level them up to try different builds.
Hope that's useful.
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