What are our goals?
Ultimately it is to destroy the barbies ASAP
To do that we need an army (cavalry) and transport (caravel).
This requires
Research - Invention (can be done in 2 with heavy scientist usage), Theology, Education, Astronomy for caravels, Gunpowder (which AI may research while we do top of tree - or is Thea more likely to do Theology whilst we do bottom of tree?), Chemistry, Metallurgy & Mil Trad for cavs. We probably have 6 techs to self research after Invention taking possibly 35-40 turns form now (less if we can get our GA).
Productive core - we need to be able to build units to transport and fight
Leo's - allowing mass upgrade of horses to cavs
GA - this will assist production and, if early enough, research (if not then commerce boost will help upgrades or short rushing)
- to get GA we need to capture Constantinople prior to building Leo's
What does war with Gil give us?
1) More territory for science farms - but I can see over 20 sites for future cities (a quick go on dot map doesnt include any S of Berwick, those near Bill are of dubious value). We only need those science farms for about 40 turns, so I dont see us being able to use all sites
2) Get him before he gets us. I admit this is an issue, but if all we are doing is positioning our troops defensively I believe we can cover him, but not if most of our troops are taking Lagash and Sumer.
3) Leader farming. This is an important aspect of having a strong enough army to fight BGs. Currently I can only find 3 elites - these need to be used to attack injured units in the open not in first wave attack - that leaves us thin on attacking Lagash - more so if they upgrade and / or build a pike (never mind growing size 6 to 7). Either Bill or Thea are less dangerous targets for war.
edit - a dot map of sorts