After beginning an Ikariam account, I initially concentrate on growth since military is not effective until the player gets most technologies and most upgrades.
I concentrate my research on science first, then economics. Gaining the science technology, letter chutes, saves a lot of gold on further research. The next technology I usually research is wine cellars so I can save wine both in consumption and building of Governer's Residences. Then I need bureaucracy to have a place to build the wine cellars. After that, I concentrate on military technologies.
There is flexibility in this order but here is one possible order to maximize growth and efficiency. The order may vary depending on the situation. I am highlighting those that I consider critical for growth and efficiency.
Research fields:
Seafaring
Economy
Science
Military
1. Economy:Conservation (Level 1 - cost 12) Allows building warehouses. Warehouses allow more storage of material and protect from pillaging.
2. Economy:Pulley (Level 2 - cost 24) Saves 2% on building costs.
3. Economy:Wealth (Level 3 - cost 112) - Allows production of trade goods and provides 130 of each luxury resource.
4. Science: Well construction (Level 1 - cost 24) - Additional 50 housing space and happiness in the capital city.
5. Economy:Wine culture (Level 4 cost 336) - Allows building of taverns which is needed for population growth.
6. Seafaring:Carpentry (Level 1 - cost 8) - Allows Carpenter's workshop discount building for building material.
7. Seafaring:Expansion (Level 5 - cost 336) - Provides the ability to build plaices and governor's residences which allows more colonies.
8. Science:Paper (Level 2 - cost 30) - 2% more research points.
9. Science:Espionage (level 3 - cost 420) - Allows hideouts which are necessary to prevent enemies from being able to spy out your armies and resources.
10. Economy:Geometry (level 6 - cost 2236) - Saves 4% on building costs.
11. Economy:Architecture (Level 7 - cost 3672) - Allows building of architect office which reduces marble used to build in the city.
12. Economy:relaxation holiday (Level 8 - cost 7200) - Increases satisfaction in all towns.
13. Science:Ink (Level 5 - cost 2652) - 4% more research points.
14. Science:Mechanical pen (level 11 - cost 31968) - 8% more research points.
15: Science:Letter chute (Level 13 - cost 144720) - Saves 3 gold upkeep per scientist.
16. Economy:Spirit level (Level 11 - cost 25632) - Saves 8% on construction of all buildings.
17. Economy:Wine Press (Level 12 - cost 48000) - Allows building of wine cellars which saves on use of wine by citizens and cost of wine for buildings and cooks.
18. Economy:Bureaucracy (level 14 - cost 106560) - Provides an additional building space in all cities.