Precursor Advice
There will be new content related to precursors due to the collections that will give one precursor per weapon type per account. I’d wait for that to come out and influence prices if you aren’t willing to do the stuff to complete the collections.
To answer your questions:
Dungeons are still a very good way to get gold. Every explorable path gives you at least 1g upon completion (once per day), but some give more. AC paths give you 1.5g per path. The Aetherpath of TA gives you 2g. Paths 1, 2, and 4 of Arah give you 3g. So, really, you could do any dungeons you want. The fastest ones tend to be AC 1 and 3, CM 3, SE 1 and 3, and COF 1. However, you could add some of the “longer” easy ones (they’re not really much longer) such as CM 1, all paths of COE (these paths give you chances at charged cores/lodestones, too), COF 2, the two Nightmare Court paths of TA, and HOTW 1. It’s just really what you feel like doing.
Yes, dungeon exotics can be forged to make precursors. I’ve gotten one from dungeon exotics before. But I believe that forging rare greatswords tends to be the most cost efficient way of getting a precursor. So, it’s up to you whether you’d want to forge rares or exotics.
Both dungeons and Silverwastes are great money, and you get champ bags from both. So, it’s just up to which one you want to farm.
As Seera said, precursors will be given for completing certain collections in the upcoming expansion. So, if you plan to get the expansion, it might be a good idea to wait until it comes out to worry about a precursor.