I don't think you need to. There was an early mission I would re-do when a new character showed up, just so I could try the character out to see how everything worked. I re-did some others just because they were fun, too. There's a "violent" one late in the game where the mission itself isn't too hard, but there's an opportunity to get a pet dragon in it that is plenty hard. I tried that one several times but haven't got one. Yet.
No pets yet, theres a ton I havent seen so far for sure. Been picking up as many loot crates in the missions as possible but I'm not sure how important it is to get everything, crafting stuff isn't really clear to me yet. I'll muddle through most likely.