Now that I've seen your list
@Dursland , I suppose I'm going to add what I've always recommended to new(er) players but it may surprise you to know that the Arc is not only not on that list but I strenuously discourage players from trying to take on that monster (or other high-era GBs) until after they've played for about 6 months + established a sound economic balance in their young cities. So here goes:
@Ranger37 Essentially, you want to address all of the needs of your city so you need to think of it's needed resources: Coins, Supplies, Goods, and FPs. Also, you'll want to consider the boosts that GBs offer that aren't usually offered in regular buildings that are obtained through your tech tree and haven't yet earned in your event items. (This is for players who are interested in both fighting and goods acquisition for general use such as negotiations, trading for higher goods, etc.)
- Fight Trio with Zeus being your first: aka CCZ (CoA/CdM/Zeus) BUT - built in reverse order! These 3 give you unit ATTK/DEF and should last the life of your city. Zeus=unit ATTK/ATTK-D, CoA= unit ATTK/ATTK-D + Coins, and CdM = unit ATTK/ATTK-D + FPs.
- LoA = Goods/Supply boost. Many players do not recommend this GB but it's a great 'starter' GB (and is useful in later eras as well) and it's Pros are that it is small, 4x4, will provide you with 40 charges of an increasing % boost based on level.
- ToR = Relic Hunt - if you don't plan on participating in the Guild Expedition, this GB is useless to you but it's an undervalued GB for those who 'dabble' in the GE. There is an excellent write up in the Fandom Wiki on it (on all of the GBs, actually) but this one has excellent charts which will help you decide how high you'd want to level it based on your playstyle and preferences for types of relics as it's point of return is different depending on the type of relic more than just the chance of earning them.
Believe it or not, that's it. 5 GBs and they will answer every need your young city needs: Coins, Supplies, Goods, and FPs. Level them all to 10 then keep going round and round and the ultimate level is completely up to you.
Now - the big, bad question: But what about the Arc? What about the CF? That's up to you. Do you want to be struggling all of the time trying to level up GBs that were meant for higher eras and really only help you if you literally ignore EVERYTHING but one or both of them? Okay, here's the scenario: we're guildies and you've just asked me, the experienced player and you are bound and determined to get one or the other or both. So, what do I say? Sure. Pick one. Just one. Look at them both carefully and decide which one is going to answer the needs YOU have based on your level of activity in the game itself, the guild you're in and how active you/they are in leveling GBs, availability of prints, and what you see yourself doing in the game in about 4-6 months.
Why? GBs are the single biggest investment of your time and of your FPs. If you take on too many, you'll wind up with a city full of GBs that are not giving you the full value of what they're worth because young cities are not prepared to level them all. 5 basic GBs are hard enough to level on the expected income of a young city in lower eras. IF you are determined to pick one of the higher era ones, I'd say oh, absolutely choose between the Arc or the Chateau simply because they are your best return on needed commodities (resources), however, DO you need a smaller than break-even return on your FP investment if you're not willing/able to invest in other GBs? (Arc, delay it if you can't answer emphatically, YES!) WILL you commit to performing quests regularly and flipping your RQs? Yes, Build the Chat! No? Don't bother, it's not worth the ground it sits on much less what it takes to get to a level where it will pay you enough to justify it.
What are my options besides those 2? Well, the Chateau is a hotly debated GB - but pretty much everyone will tell you to build the Arc. When is the key question: when your daily FP income is stable and your stable of GBs and your basic resources are stable. AND you have a reliable - very reliable - way to invest those FPs you've spent such a long and hard time earning.
I love my Traz but I have to say that if you only intend to fight in the expedition and even in bg (battlegrounds) then don't bother. Wait. It's the biggest footprint of them all at 10x7 and until you can level it produce enough units to exceed what you are using per day then it's probably not worth the loss of space or FPs to have it. Many, many players are more than able to meet their unit needs by judicious placement of racks (barracks) and by earning units in the expedition and battlegrounds. (Once you've obtained enough unattached units through playing the GE and BG, you don't really need to have a barracks for that type of unit in your city unless you are running low on them or plan on camping in a particlar era). Now, having said all of that - IF you are going to play GvG, having a Traz could be in your future sooner rather than later but only if your guild is requiring you to perform fills. A good guild is not going to expect that from a new(er) player or shouldn't.
Try to remember the most important thing about any GB: They can be your best and most useful tools to make your city more profitable and stronger in terms of fighting but they are also space-hogs (and because of that can become your worst enemy!): think of each one by how many tiles it will use in your city. Traz: 70 tiles. Arc: 35 tiles. And so on. Every one of those tiles 'could' be used by something that's actually doing more for a young, smaller city (lack of expansions until you've advanced eras, etc.)
Last but not least on the Traz: so many players forget to tell the other person that really, really wants a Traz this part: you don't just need the 70 tiles for the GB itself, you need enough tiles for each and every barrack you'll need to place for the Traz to choose from. You have no barracks? The Traz will produce nothing. (Not saying to build every rack in your era - you can always rotate them out to keep your units balanced, but even 1 or 2 racks PLUS the Traz can literally eat up all of the ground in your small, younger era city and then ... you've got some serious problems on your hands!) Okay, sorry that was so long - but here's the best part! DO IT YOUR OWN WAY!! It's your game and your city and you've got to be happy with your choices. GBs might be hard to get and harder to get them where you want to but they are still just as disposable as anything else you put in your city should you decide you either made the wrong choice or just plain don't have the use of it anymore.