I didn’t play any of the single player missions during the beta because I was more interested in the multiplayer. I have heard that you can get gear as a reward for completing the single player missions; how exactly does this work? Do you get gear packs that are exclusive to each mission after completing said mission? Or do you just get random gear packs after completing any mission? The reason I am asking is because I would be willing to purchase the deluxe edition if the included single player missions will feature exclusive gear as rewards for completing the missions, but if you can get any gear by completing any mission, then I see little reason to purchase it.
There’s a little of both, plus some.
You get some gear packs as drops, which is shared with your whole team (so no loot ninjas). You also get random loose gear, which I believe is also shared. And last, with every boss, there’s a unique legendary they can drop. This is shared, as well. It’s a pretty awesome system, truth be told
There are small pick ups that are found in containers. Pick them up, and you get some loot packs if it’s the right one.
I think defeating a boss nabs you a singular piece of loot, as well.
Ah, I see, so that’s how it works. In that case, I’ll definitely be picking up the deluxe edition. Thank you for clearing that up.
No problem 
Happy to help you make an informed choice
IIRC, once you’ve unlocked them by level, there are also loot packs you can purchase within the command centre using the in-game credits. So, several ways to get gear.
True, but I don’t think you can get the exclusive legendaries from packs, plus the packs dropped in campaign are usually green or blue (from what I’ve seen gotten) so PvE will get you better gear faster than buying packs
You in fact can acquire legendaries from store packs. This is first-hand account. Got a VERY nice legendary that gave splash dmg to skills.
Should mention that the item was from a themed pack, Jennerit. I would shoot blind and assume that there is probably one, maybe two if lucky, legendaries that follow what theme of the pack you buy. So while one might think the theme packs aren’t as good, they offer a wide range of goodies.
You can also get purple pack drops in story, and though costly, buy purple packs from the store.
That’s pretty much my experience to, although I never got as far as unlocking the Jennerit pack. Had some interesting looking gear by the end of the weekend!