What is main advantage of going corps?
Most powerful endgame cities possible. Full corp spread in Free Market with Sushi+Mining, Free Speech + US beats hammer economy
What number of resources make it worth it?
Depends on the corp and the goal. Sushi is for growing cities, so as many seafoods as possible is always what you want. Mining Inc gives 1 hammer per resource IIRC, so I would want like 5-6 at least to get raw hammers that become 8-12 with all buildings in place.
You either want mining or Sushi. Maybe Cereal?
Sushi is always the best corp because of the volume of seafoods + seafood clustering/redundancy AND Rice as well, which leads to large amounts of yield especially on island/watery maps. Mining is more supplemental, but it is the second best corp as it's most extensive on what it collects and gives a large return per resource. Next best would be Creative Constructions if you miss Mining.
It's important to consider that if any corporation collects even a single resource that is the same as collect by another corp, it "competes" with that corp and they both can't be in the same city. If you spread Cereal, which uses Rice, you can't ever put Sushi in those cities unless you supplant Cereal with it.
AIs will also instantly refuse to trade resources for your corps if they need those resources for their own corps, meaning if they found a competing corp, you'll lose the resource trades that are covered by both corps. So Sushi and Mining are also better because they have more extensive resource lists: Nothing competes for Sushi's seafoods, Mining can collect a lot of resources from many sources for large yields even though all its resources are contested, Creative Const. has 2 resources that are unique to it and one (aluminum) that is rarely contested even if it's weaker than Mining, etc etc. Mining Inc. is the most contested corp, eventually if all corps are founded you'll lose AI trades for every resource.
This all paints a picture that corps are best used when you can control the competition directly, hence Score and HoF game usage.
I guess the idea with food is to spam specialists? Mining for hammers?
Grow cities with Sushi for higher pop to win diplo or to get high scores. Sushi also gives a lot of culture, though that shouldn't really matter if obliterate the AI and oyu can win Culture faster without ever looking at a corp. Mining is mostly to offset the loss of workshop power, but it can make even crappy cities (like island heavy maps) very good with enough resources
I forget how you deal with spiralling city costs.
Run Free Market, found HQs in the Wall Street city, courthouses everywhere.
Domestic Corps and Foreign Corps
Domestic Corp - you spread this to as many of your own cities as possible to benefit from the yields of the corp itself. Sushi, Mining, etc.
Foreign Corp - you have this corp in one of your cities, and spread it as much as possible to AIs to get income. Ideally a corp that competes as little as possible with your domestic corp so spreading it doesn't weaken your resource trades. Aluminum Co. is the best, followed by Ethanol for this purpose -- both use Scientists to found and only compete for one resource of Mining/Sushi respectively.
Put your Foreign corps HQ in the Wall Street city, and then the HQ of one of your Domestic corps there too (whichever one doesn't compete with your Foreign corp). Put all gold buildings in the HQ city with Wall Street. Spread your domestic corp that is in the Wall Street city to all of your cities, the extra Wall Street gold will minimize expense impacts. If you have another domestic corp, it will cost you more net to spread it everywhere since it won't pay the HQ costs through Wall Street for 100% extra gold, you have to found it in a different city.
This all assumes you are even leaving the AIs around to play with in the first place.
