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Briefly, each ship can fall under one of these categories: Civilian ships, Drones, Small/Medium ships, and Capital ships. Simoon wrote a guide for capital ships for Rebirth v3.00 and although it is a little outdated now, it may be interesting background with that caveat in mind (link).

Advantages of Small/Medium ships are higher in-zone speed and lower cost, but coming with the disadvantages of weaker defences and cargo type restriction (although this isn't consistently an issue). Advantages of Large/Extra Large ships typically include sturdier defences, greater storage capacity shorter travel times between zones/sectors/systems*, and the option of ships that can carry two or all four cargo types. Downsides of the biggest, strongest ships compared to smaller Large ships include slow include longer overall delivery times** and the potential for all their cargo space not being needed for a given run.

 * Facilitated by point-to-point boosting within a sector, and a Jumpdrive for inter-sector travel.
** Caused by slower align times and reduced boost speed as it is a standard multiplier of slower base speeds.

Ship construction materials

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