I think everything you work toward should be beneficial.
For instance:
Claiming a camp: Doing so will cause scouts to gather floral and hunt around the area of your camp, causing you to get a cache of leather and herbs with each camp claimed. (and not just six)
Closing Fade Rifts: This will result in Fade Touched materials and the "rarer" ones will be determined on the level of the rift and the area. Example, if you're a high level in Emprise de Lion, closing a rift will get you Fade Touched Silverite or Dawnstar--if you're a lower level, you'll get FT Bloodstone or cloth.
Claim a Logging Site: This could also result in scouts gathering flora and leathers and native metals by clearing the site to ready it for logging.
Claiming a mine: This should be obvious, claim a mine, get a cache of local metals and depending on your level or influence, include some rare or FT.
The more agents you recruit should allow you to send certain agents out. For instance, Scouts for Leliana can be sent via War Table to gather plants or secure crops of a certain herb. (And not the shoddy six plants they usually gather, but the amount and rarity will be dependant on influence/level, Josephine's agents could procure you leathers and cloth from merchant deals, Cullen, metals, etc.
And as Tom said, Dagna would be a wonderful resource to help gather rare materials such as Fade Touched Items and other Masterwork materials. She has to have some contacts from the Circle and from merchants who sell "special" materials.
Instead of clearing an area and recruiting people to "Spread the word of the Inquisition", you can literally hire them to mine, grow crops, hunt for pelts, etc. The rareness and amount again, dependant on how much influence and experience you have.