The higher and rare the reward, the most resources it costs and the much expeditions you will have to complete to get them.
Don't spill expensive resources like pale steel, bricks, scholarly fragment or soldier pine in expeditions.
Stockpilling the Pantry / Cellar / Smokehouse
Doing those expeditions aren't really worth it as you turn precious resources like wood and soldier pine into boxed food.
If you really need to quickly turn your food into boxed food because you can't do anything else to protect them, use the expeditions. It's better to lose a small amount then all of it!
The Vitner's Goblet
Do the expeditions that costs you only basic resources like food, wood, stone and iron to earn Vintner's Cask. You need them to craft the trinket Vintner's Goblet (increases march speed and training capacity).
As there are a lot of other gear you can combine to increase march speed and training capacity, it can be a waste of time and resources to do those expeditions to craft that single piece.
Bricks / Soldier Pine / Scholarly Fragment / Pale Steel Shard
Do the expeditions that costs you only basic resources like food, wood, stone and iron.
It's preferable to hunt instead of complete expeditions for bricks in the beginning. When you need huge amounts of brick and can't get enough with hunting, begin the expeditions.
Dragon - Mustering of Livestock
Do the expeditions that costs you only basic resources like food and wood.
Do the expeditions only if you don't get enough food with hunting and gathering.
King's Landing
Merchant's Guide > you can get Keystones but you have to pay the price with basic resources and another expensive resource like scholarly fragment / Pale Steel Shard / Brick or Red Gold Flake.
Traveler's Guide > you can get Red Gold Flake at the same conditions.
On those maps there are no expeditions that costs only basic resources as the resources you earn there are a lot more expensive and can't be bought in game to level up buildings and complete researches.