I feel like this is something I've gotten a better feel for. I'm sure some of the strongest always-win-on-Deity players have clear rules for what they do and don't do, but for now I still kind of feel my way forward in each game. The biggest breakthrough for me was to realize that the Eurekas don't need to be accidental. Pursue Eurekas on both Techs and Civics with an eye to your long-term goals. For instance, a well-timed builder can knock out about four Eurekas in 3 builds if you have the right resources. A well-placed second university will knock out two Eurekas. Here are three symbiotic good early--to-mid-game Eureka Research/Build sequences that you shouldn't necessarily beeline, but that you can pursue fairly quickly as part of a balanced research approach (you'll need to research some other prerequisite technologies for these, but keep the Eurekas in mind to speed up your research):
1. Build 3+ Slingers > Kill Barbarian with one > Research Archery > Promote 3+ Slingers to Archers > Research Machinery > Promote 2+ Archers to Crossbows > Research Metal Casting > complete trees 2 & 3 >
2. Kill at least 3 Barbarians > Research Bronze Working > Build Encampment > Build Barracks (or Stables) > complete tree 3 > Build Armory > Research Gunpowder > Build Niter Mine
3. Research Mining > Build Quarry > Research Masonry > Build Ancient Walls > Research Engineering > Build Aqueduct/Baths > Research Military Engineering
4. Follow Tree 3 through Engineering > Build two Catapults > Complete tree 1 > Promote Two Catapults to Bombards > Research Siege Tactics > Build Siege Engineer > Build 2 forts > Research Ballistics > Promote all Crossbows to Field Cannons.
You don't have to follow every step here to max out the Eurekas. It won't always make sense. Sometimes you skip Encampments, Barracks, Armories, Catapults, Bombards, Siege Engineers and Forts. But if you generally follow this strategy, you'll end up with a fast-developing tech tree and some very useful units, buildings and resources pretty quickly. Because I don't see a clear way forward with Eurekas from these same units afterward, you'll also want to follow the Melee, Cavalry and Naval advancement strategies, which pay off more later in the game with bonuses that lead to Electricity, Replaceable Parts and Military Science, among others.
