[Allan Hood]

Which sector should I go to find the best Dilithium Doff missions? Do people craft their own weapons/shields or do you go to the Exchange?

[Spaceland]

I find that the best dilithium comes from Admiralty, Rep boxes job. 340 dil per boxes, per hour.

Or if you have time, undine battle zone space or ground. When busy you get around 2k dil after map done.

[zoidberg]

Best way to do is to get daily klingon admirality.Kligon admirality gives you 30k after 10 days and ground elites gives you 1400 after each run

[Dark]

I just DOff everywhere. Aside from the Fleet Mine and the normal set of 50 Dil assignments, as well as colonization sector ones requiring Colonists, I haven't noticed anything with particularly high payoffs. The area around DS9 has the rare commodities ones, which have related turn-in assignments. The latter seem to spawn everywhere though, just be sure not to waste the commodities on the turn-in assignments that give 5 Dil.

The 2nd best weapons are still crafted.

The absolute best (afaik, could be out of date) are from a Lockbox (Coalition Disruptors?) and require an exorbitant amount of resources due to the modifiers being random. So you need a ton to get the ideal mods.
After that are the crafted weapons, where you keep crafting Mk II weapons (relatively cheap) until they have three ideal mods, then upgrade them in the hopes of picking up the ideal 4th mod. If it doesn't pick up the ideal mod, toss and repeat.
The next best after that is the most cost effective, picking up Advanced Fleet weapons with [Dam]x3[CrtD] mods.
The ideal mods for a Tac captain is [Dam]x3[Pen] followed by [Dam]x4, so the Advanced Fleet weapons are close. For non-Tac we want [CrtD]x3[Pen] followed by [CrtD]x4, so it's slightly less good - though keep in mind the differences here are around 1% DPS.

For the set gear (Shield, Engines, etc.) we haven't been crafting those since the reputation sets came out back with the Borg 4-piece from STFs. Aegis did get buffed a little, but it's strictly inferior for practically every role (aside from looking cool).

The only consoles we craft are the Science ones (with Part Gen mod) for Science wizard types (and I don't know if that meta survived the revamp), and the Engineer ones (with Power Transfer mod) for pewpewing. These also take a horde of resources due to needing to be crafted at Mk XII, yet having random modifiers.

Oh, and consumables - some of the best consumables are bound on pickup, and are from the crafting system. The Eng consumable heals hull and gives temp HP, handy for everybody. The Beam/Cannon consumable gives a Weapon Power buff as well as a damage boost, and is (afaik) better than Weapon Batteries as an offensive boost. Not sure about the other stuff as I just run a beam boat.