In regards to +1 production per city and % based cards you will be surprised...You only need 4 Cogs per city for the Builder Card to overtake(or 3 with surplus amenities) the +1 production Card and of course the military cards are even better. The +1 production is still good but its value is more when you have a diverse group of things you are building rather pure efficiency. If you are building lots of buildings it makes sense to go the +1 production card, as their are no better alternatives. However if you are building builders you should consider switching to Ilkum, even your smallest cities will probably break at least even with Ilkum instead of the +1 production card. Agree with banking builder production as well and also to pre build builders with Ilkum and then switch in Serfdom to get the benefit of both cards.
@ OP
My First couple of games was with Rome and i feel ya about feeling lost. I was burning through the Civic tree so fast due to trying to REX that i kept on getting lost too
. One thing is always prioritise the center of the Tree. Political Philosophy/Feudalism/Civil Service/Nationalism Etc. If you teching it to early that is cool, just pre-tech and then wait for the Inspiration. Hard tech troublesome Inspirations early. Like the Defensive Building one that is required for Fuedalism. If you don't already have the inspiration dont sit around waiting to get War Decced on, just hard tech it unlocking Civics that are much easier to get inspirations on etc. Same with Nationalism, If you are going to struggle to use Casus belli dont bother...beeline it and hard tech it early, same for the one that requires an Alliance. These Civics are too important to pussy foot around with Inspirations, not so much the Civic itself as for unlocking the next part of the tree.
Also be careful of the Bottlenecks. It is very easy to get caught putting off Civics, trying to get the Inspiration and been left holding the Bag...forced to Finish Hard teching the Civic because you simply have nothing left to research, wasting the Inspiration(and more importantly all that time when you could have it researched already
. Bread and Games/Drama and Poetry is a good example, sometimes you just have to bite the bullet and hard tech it, allowing you to inspiration save other Civics. Another good idea is to Look for Civics that aren't usfeul to you in particular and bank them for easy Policy Changes. Some Policy Cards such as Surveying(20% off tile buys) can be maximised within a couple of turns. It is incredibly handy to have a quick 3-5 Turn Policy to use to quickly get in and then out again.
O/T Few Builder related Notes...
Ilkum stacks with 15% Wonder card and the Pantheon with China. With both The Pantheon, Policy Card and The Pyramids China gets a Single Builder 5 turn Ancient/Classical Wonders..... Sooo Good. Build Builders with Ilkum and switch to the wonder to rush with the builders every turn. Of course you need Classical Republic or Oligarchy to make it work. (2 economic slots). You effectively get every Ancient/Classical Wonder for the price of a 30% off Builder
(After Pyramids...You really want that lone one tile of Desert in your Capital as China
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As Monty dont be so quick to use your builders on Districts. Mainly in your core producing Cities. It could very well be a net-loss in regards to hammers. It is useful of course to use your core cities to build builders which then rush districts in your startup Cities but if you are just building builders to rush districts you are effectively increasing your builder cost for very little hammer gain...Do the Math