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TEC
...if you prefer managing your empire to micromanaging your fleets.
They're also nice for starting players and the economic powerhouse.

Advent
...if you like to focus on the fleets and combat. They're a bit weak in economy and the ships a bit flimsy, but if you manually control the ships' abilities and combine them, you can beat much bigger fleets.

Vasari
... if you like tactical cat and mouse games and mobility. Their ships are strong, have abilities that make them good for raiding deep into enemy territory, and with their phase gates, Vasari fleets can quickly reach any part of your empire.