Ok, so following on ODragon's answer, its a matter of priority, so the short answer to my question is that a smart player does not level the CDM past 10 until all other better options are exhausted, which according to him are things like Shinto Temple, Royal Bathhouse, Arc, CF, Cape. So once I have all special buildings and the aforementioned priorities leveled, only then would it make sense to start leveling things like the CDM, Zeus and COA. Is that right?
Sort of. Working on getting normal (non-GB) buildings like the Shinto Temple is something we do at the same time as working on our GBs. Only once the city is jam-packed, do we have to start making a trade-off between normal buildings and GBs. (And BruteForceAttack is right - the two most important things are FP/day and attacking army boost. So there's also a trade-off between those, both when it comes to normal buildings and when it comes to GBs.)
So, if you're new, you should be trying to get useful buildings from the event, and from the daily challenges, and from the settlements, and from GBG and GE. But at the same time, you should also be trying to work on your GBs, both by acquiring blueprints and goods for ones that you plan on building, and by spending your FPs leveling the ones you've already built.
For a new player, I'd advise working on 3 types of GB at the same time: a) working on getting an Arc built and to level 80, b) working on getting your SoZ built and to level 10, then your CdM built and to level 10, and then your CoA built and to level 10, and c) getting an Obs built. You'll find Arc and Obs blueprints are harder to come by at first, so you'll probably make more progress on the SoZ. Also, the goods for building an Arc will be much more expensive than the goods for the other GBs. And then you'll need 70 more full sets of Arc blueprints before you can get it to level 80. (And in all that, if you find you're running low on supplies, try building the LoA and working on it a bit, too.)
They say that this game is a marathon, not a sprint. But the game is also about trying to do a dozen things at the same time, and not letting them get in the way of each other. ;-)