Ikariam research - recommended research path

In Ikariam research is the main way to advance your civilization. There are four main streams of technology to research: Military, Economy, Science, and Seafaring. You need to assign citizens to the Academy to get research points which you need to invest in researches. Well Digging should be one of your first researches. It gives you a morale bonus and a bonus to your population cap, which is very important when you're just starting your town.
Next, Conservation is also important to research as it will allow you to build a Warehouse. A Warehouse will protect some of your resources from being pillaged if someone is attacking you.
When you get access to grapes and wine, you may build a Tavern. This will boost your town's morale and thus giving you more people in your town to either put to work or to gain gold from.

When you first start playing Ikariam research can be a bit confusing, but there is a clear path that is recommended at the start of the game.

Well Digging → Conservation → Pulley → Wealth → Wine culture
This way you expand your town as quick as possible, with the bonuses from Well Construction and from the Tavern. It will give you access to luxury goods and you will be able to trade with other cities. Next, you could follow this path:
Dry-Dock → Maps → Professional Army → Deck Weapons → Ship Maintenance → Expansion → Paper → Espionage → Foreign Cultures

Professional Army gives you access to, among others, the Hoplite, a basic unit to defend your city, but the Hoplite requires a level 4 Barracks to build. If no one is attacking you, it is possible to postpone this research.

Expansion is crucial to obtain, as it will allow you to found your first colony after building a palace. These are the basic researches you should obtain in the beginning. Other researches you should aim for are Cultural Exchange, to further boost your town happiness by building a museum, and Helping Hands, to increase production.

Remember to constantly upgrade your academy as your population increases. When you are not able to do so, due to a lack of Crystal Glass, wait until you finish researching wealth as this will allow you to trade with other players.