Evaluating BFA currencies for missions

TLDR: 

1 gold = 0.25 WR = 1.7 rep (1.25 Honorbound/7th Legion rep) = 0.01 service medals. AP is close to worthless.

The long version:

Gold: our base currency. Can be exchanged for a great many useful items and resources.

Artifact power: this is a personal upgrade that can't be traded. With 8.2 it looks like it will become redundant, so long as your necklace has reached level 50. That seems very easy to reach. My alt who I've never deliberately done anything just for AP already is at level 46 a couple of months after hitting level 120. I'm expecting all 3 of my alts to hit level 50 before 8.2 or maybe soon after simply by doing missions and emissary quests. It's still worth doing AP missions from the table because you want the procs from your follower equipment.

War resources: The game seems to value WR at 4 gold per. A world quest that awards about 160 gold awards about 40 WR. The value of WR depends how onerous it is to farm this. With my main he has been WR positive simply by having all Exalted reps and the mission table advancement Azerothian Diplomat. However he can cash out excess WR by sending them to a less advanced alt so still pretty useful. Eventually the value of WR will go down once every alt that runs missions is fully advanced. Currently I do run WR world quests on my alts so I value WR at significantly above 4:1 because I'd not do a world quest for 160 gold. Part of this is preparation for 8.2 and partly this is developing this multi-alt mission table farming set up that I'm expecting to be an important part of late BFA gold. Let's say this may be valued at 5:1 while you're developing your mission runners or running out of WR when continuously running missions. If you find yourself skipping missions because you've run out then you're missing out on 2*226 gold from Follower Equipment procs plus 150ish gold value for a base mission for the want of 20-80 WR.

Paragon bags: 4000 gold, 500 WR (worth 2k), 2500 AP (nice but not really worth anything). So 6k for 10k rep which means 1 rep = 0.6 gold. (We'll discount the pets for now).

Reputation: 0.6 gold. We can use the paragon bag-derived value because all that matters is rep at the end of our BFA gameplay. Let me explain: suppose a mission runner will earn 85k rep over the course of this expansion. If you were to add an extra 10k that would add an extra 6k gold value. It doesn't matter that you had to sink 42k rep before she got on the paragon gravy train. There's no option to not invest that rep if you're doing emissaries and missions every day.

One world quest. The baseline for doing a world quest should be the opportunity cost of not doing an item world quest on my enchanter. One epic item disenchants into a Veiled Crystal, currently worth 360g and likely to hold its value into 8.2. (occasionally you get an Umbra Shard worth 180g as well). So if you're doing world quests that pay out less than 360g and not doing them on your enchanter you're not being efficient. This means that these WR quests I'm doing at the moment to get my alts through the mission table advancement are worth more to me than 360g, a value of 9:1. I would do a world quest for 40 WR and I wouldn't do one on my main for a Veiled Crystal. However this is a temporary situation once the alts are more self-sufficient from passives I'l stop running these quests.

Service Medals. The only way to turn these directly into gold is to sell the pet (Tanzil for Horde) but it's a pretty slow seller, mine hasn't sold in these last few months. A better way to evaluate them might be to base the assessment on the Draught of the Ten Lands experience potion. This item is extremely valuable at the start of an expansion when you're levelling your main but just a nice to have now when it's just alts. It depends how much you like the journey rather than simply wanting your alts to get to 120 as quickly as possible. It's more valuable if you stack a lot of experience impriving factors at once - DMF buff, heirlooms, Insightful gem. It's even more useful if you're getting power levelled by a friend or by paying gold for it. For me I'd put it at about 500g which means that 1 service medal = 100 gold. For most people it's probably more valuable but I do enjoy the journey. Service medals may be higher if there's another option in the shop that you value highly. I am saving mine for the ring which teleports you to the docks near the mission table. I've got it on my main and I want it on my alts because it will become particularly important when they are still running missions when perhaps being hearthed in Najatar in the 8.2 patch. There's also nice mounts and heirlooms on that vendor.

One implication of that is that the Honorbound (or 7th Legion) paragon bag is worth an additional 2000 gold for the 20 medals they give in addition to the other rewards.