Here is a speedy method (<10min) that works for every civilization, so save it for when you've finished every other achievement aside from "Here's Looking at You, Kid" (Unlock all Great Persons.)
Single Player > Play Scenario > Beta Centauri > Chieftain
Immediately change government type to Democracy for 50% gold bonus.
Place your settlers with as much water around them as possible. Ideally, you want them on a peninsula with deep water nearby, but don't bother searching if you have to use more than one turn, especially if there's already a decent amount of water right near you. Set the Modern Infantry to defend the city after building it.
Switch production to gold only and build status to Market. Now just skip turns until you have enough gold to rush build the Market. You will get bonus Settlers at 100 gold, but you should just settle them back in your city to increase the population faster.
Then just collect gold and rush build these in order:
Harbor (to increase population quicker)
Bank
Courthouse
Temple
Cathedral
Hanging Gardens of Babylon (instant 50% increase in population, which will increase gold production quickly rather than waiting for natural population increase.)
Now wait for 20k gold
After getting 20k, rush build a Factory, set max Production, set to build World Bank, then finish skipping for your easy Economic victory. You can optionally set government to Communism to save 1-2 turns, but it probably takes more time to change governments than to just let the game finish skipping with Democracy.
Also, Activate/Wait any Great People that you get except Scientists, which you want to use to complete Future Technology (bonus trade.)
The important part to making this speedy is not exploring at all or making contact with any other the other civilizations. Barbarians will make initial contact as you build the Courthouse but will otherwise leave you alone on Chieftain difficulty. Most of the time you will not be discovered by other Civilizations, but when you are, the process becomes a little slower since you will have to skip through extra dialogues and watch their unit movements. If this happens, it will most likely be after you're waiting on the 20k gold. You can build 2 extra Modern Infantry to form an army if they're making you uncomfortable, but 1 unit is almost certainly enough since I went through this 12 times and was only attacked 1 time (with no problem since Modern Infantry already has strong defense.) As long as there are no events going on, the game will continue to auto-skip, making it go very fast. Typically, only messages from your advisers, appearances of Great People, and city population increases will prompt you to press B to skip more.
When done correctly, each play will take 6-10 minutes, with some variations due to the bonuses attributed to each Civilization.