Constructive & Helpful!
I take it that I can't manipulate the "at random" quests but I can max out the reagents to manipulate "receive one of the following".
Yes, in the case of "you may receive at random", every drop has an individual drop rate, independent of what other drops you already have.
In the case of "you may receive one of the following", it will give you 1 random drop, but if you already have that drop, it will try another one and so on until it can find something you don't already have maxed out in your inventory.
And the Tendurr Dailies, i saw, god good rewards. Which should I prioritize, or rather, which reagents hare generally tougher to gain with other quests, that I can accelerate with Tendurr?
Of the ones on the "you may choose" category, you should probably use it to get Dark Crystal Shards or Gems of Nulgath. You wont be getting Gems of Nulgath regularly by doing Supplies/Assistant, like you would with Larvae and 10 Dark Crystal Shards is worth more than 20 Diamonds or 20 Tainted Gems, based on how long their individual quests take.
In the "you will receive one of" category, just try to make sure you can guarantee Blood Gem or Totem drops, if possible. While the Elder's Blood can be used to get more than 1 Roentgenium per day, gathering enough reagents for 2 or more Roentgeniums per day requires quite a lot of dedication and getting a couple free Totems or Blood Gems is always nice, plus it gets you closer to the cap of those items, for if you ever want to use it to get a free Uni 19, once/if you decide to farm for Archfiend Doomlord.
Is it generally better to stack all the stackable items (e.g. Archfiend's Favor to 4500x) or earn enough for each quest as I go? Or is it just a matter of preference?
You farm both Favors and Approvals at the same time, Favors stack to 5000 and are AC tagged and Approvals stack only to 1000 and are not AC tagged. I would just stack up until you have 900-1000 Approvals, which is enough for 3 turn ins and then bother with those once you run out. It is entirely a matter of preference, but it CAN be faster to stack up whatever you are farming to the max, like Emblems for example, since it requires you to not come back to the same map as often.
In the case of Tainted Gems and other reagents which drop from Supplies/Assistant/Larvae, it's generally better to leave a little bit of room for getting extra of those. It would be a waste of time to farm up 200 Tainted Gems for example and then do Supplies/Assistant/Larvae for an extended period of time, in which Tainted Gems are a possible reward. In those cases, it's recommended to not stack those items to their cap manually.