I'm done engineering all my ships (for now) but my routine used to be:
Farm HGEs in at least 4 different system states, and ALWAYS making sure one of those was a Federation system in Boom state to get Core Dynamics Composites. Nearly every ship build needs Hull and/or Armor engineering. Core Dynamics Composites go super fast when you want those G5 heavy duty mods.
Farm Dav's Hope to fill up on G1-4 manufactured mats. Not having to trade down as many G5s saves a lot of time imo.
Farm Bug Killer. Bug Killer is often overlooked. Three cargo racks with G4 Raw mats, and three scannable comms for Encoded mats. Most of the time, I never had to farm Raw or Encoded anywhere else. The only problem with Bug Killer is Thargoid Interceptors appear and annoy you by scanning everything on site. They aren't hostile, but you'll get sick of them after a while.
Farm Cubeo 3A for Selenium. Selenium is another biggie. It's used for Shields, Efficient weapons and other engineering mods. I would end my farming run by going to Cubeo 3A and getting a couple dozen Selenium in my srv, the old fashioned way.
The final step was going to material traders and exchanging mats for what I needed most for the current build. I never had to make more than one round trip to fully engineer a single ship.