War map missions with sidekicks pic on them (not 100% sure, but close to it) grant you power amulet for that sidekick. +1 skill practically. So you should do them definetly.
Klem warmap missions usually net you a nice item or schematic so those you should also do.
Many other war map missions are mostly meh, sadly I didn't write them all down so now can't say which ones are timewasters only. They net you some small cash, semiuseless item or symbollic amount of inquisition power. If only someone made the norespawn mod so I can replay the game and write them all down…
But you're forgetting the most important duty!
Killing dragons.
Hinterland dragon is pretty easy (vulnerable to ice so get Vivianne, put some ice staff on her, equip fire resistance belts on everyone). Others are a bit harder, but why you should kill them? Because almost every dragon gives you a power amulet for sidekicks and unique equipment better than anything you can craft! Oh and masterwork high chance materials, ofc.
But there is a catch. If you really want to nail those dragons easily, you *must* craft, if not armor, then at least weapons (with bonus damage against dragons runes).
IMO a beautiful strategy design. Not overpowered crafting, but still needed to get the best items in the game.
And don't forget to upgrade Varric's Bianca with crafting!
The only problem there is that inventory system is consoley_retarded so crafting can be annoying as hell.
Yes, the game offers so many things… And they ruined it by sucking up to console grindlovers.