Economics is a very important part of game play in Stellaris and the game offers a lot of flexibility in how one can develop an economy. Consequently there are many types of economy that one can develop in Stellaris. Here are a few of them.
Autarky is an economy which aims to produce as much as it requires in house without resorting to the market to make up for shortfalls or cash in surpluses. It is the default economy type at the beginning of the game and the mandatory economy of the anti-social empires like Determined Exterminators, Devouring Swarms and Fanatical Purifiers which have no access to the Galactic market and can not conduct any diplomacy.
Autarky is a fair economy in the early game because the market fee is so high and in isolated starts diplomatic trades are not possible either. Later as diplomatic trading opportunities open up and means of reducing the market fee become unlocked then specialising production for trade becomes more viable.
A cash crop economy is an economy which specialises in the efficient over production of one or only a few resources. The surpluses are then used to barter for all the other things required. A cash crop economy relies on the market and good diplomatic relations.
Pops themselves can be a cash crop for Barbaric Despoilers through selling their captives in the slave market.
Key traits, civics, ethics, traditions and techs are those that improve the output of the specific resources being specialised in and lower the market fee.
If a basic resource like energy, food or minerals is being specialised in then the authoritarian ethic is suggested for the bonus to worker output.
If a manufactured good like consumer products or alloys is being specialised in the egalitarian ethic is suggested for the bonus to specialists.
A conquest economy is simply the taking of territory and / or population from another. It is the natural complement to Autarky for Determined Exterminators, Devouring Swarms and Fanatical Purifiers. This economy tends to a wide playstyle. As with any military economy its success rests heavily on fleet power so the most critical elements for production are alloys, energy and naval capacity.
In this economy the substance of income comes from resources coerced from tributaries by means of overwhelming military force. It differs from the Conquest Economy in that no territory or population is taken only taxes. This economy is the go to for military powers playing tall as it is highly sprawl efficient.
Key traditions are Supremacy and also Diplomacy. Key techs are those that increase naval capacity and unlock new ships and starbases. Pops are primarily employed as soldiers and metallurgists. The soldiers expand naval capacity and the metallurgists turn mineral tribute into alloys for new ships.
See my article The Grand Fleet for an example empire build which specialises in this economy.
A prospecting economy is one that invests heavily in science ships to find the very richest systems first and claiming them early. Anomalies can yield many resources from ships to techs which do not even require the system to be claimed.
In this economy leaders are more important than pops and is particularly suited to a defensive tall playstyle.
It is strongest in the early game but runs out of steam as the map fills up. Gradually it becomes a claim camping economy whose success depends on camping on, and successfully defending, the value of the early finds.
Key traditions are those in the Discovery tree. Key civics and traits are those that buff leaders. Key techs are those that improve research and mining stations and unlock mega structures.
There is no means to trade technology for resources in Stellaris so strictly speaking a true knowledge economy is not possible. It is possible however to strongly specialise in research and then leverage the technological gains later for economic and military goals. This economy would be synonymous with a tech rush strategy.