You have predesigned ships... But it is often better to create ships yourself.
You can always upgrade your own ship when better version have been researched.

Oh yes, if you want to keep old ship things on the ship when selecting upgrade (so you can see for yourself if upgradring is worth it) you have to deselect the option in the option screen...

Some techs though have a passive bonus. Impulse I, Warp I, and Hyper-Warp I, for instance give all ships already built and ones to be built a +1 movement bonus.

The first sensor tech gives all your ships a +1 sensor range bonus.

Ignore the core ships, they are to slow! You can always design a better ship yourself at the same tech level. At game start (even before researching new techs) you can design a faster colony ship than the one you start with; send the one you start with towards a nearby planet and start build a faster one on your homeworld! Once you have impulse engines and sensors researched you can build a better survey ship than the one you start with for exploring anomalies. Look at what the weapons and defenses the AI is researching. Ideally you want to be researching a weapon no one has a defense for and researching defenses to counter your enemies' weapons. Then design custom warships tailored to your enemies' ships.