If you are curious when it is a good idea to aim for one of these farms over just focusing on getting great people through age progression then simply ask yourself whether sitting around and building a farm is faster then starting a new run and is it more fun?

If yes then go for the farm you want, if not then reset and come back when your ready.

Classical & Middle
Faith

Renaissance
Bonds

Industrial
Stocks
Ironclads

World War
Battleships
Diplomacy
Submarines

Cold War
Tvs
Spacecraft
Aircraft Carriers
Nuclear Submarines

The most common farms I see are...
Bond
Stock
Diplomacy
TV
Spacecraft

That does not mean the other ones are not viable, it just means the most active players like to use these farms and advertise the Empire Value generation they give.

Summarized tips for convenience:
Farms from later eras = more EV per a second
but depending on your gp situation moving up might not be a good idea right away.
Since why spend months for a spacecraft farm for a few hundred gps when you can get more from a bunch of lower level farms you are doing in the same amount of time?

It is a good idea to play on Babylon for your first time doing a farm because it is easy to maintain a +7 to +10 production boost to almost every building you got. It could mean less buildings but that +7 alone is worth it! If not then just disable the "Ziggurat of Ur" and enjoy a +3 to +6 boost to almost everything. The catch is this is a supporters map, so it might not always be available to non donor players.

I personally stuck with stock farms until the Cold War was released then bee-lined to spacecraft because I was ready and bored of my 2 day runs.

Keep an eye on the market because someone might buy what you produce.
Free EV is free Ev after all.

Why are there no farms for the early eras?
That is because players at these stages prefer gps through age progression not EV acquisition.

If there are more farms that I left out feel free to include it below and I will add it to the list of farms.