At the start, I had 2 6kton naval shipyards for my fleet as well as a commercial one for jumpships and a large 10kton naval one for a sensor ship.
As the game goes on, I added a 6kton naval shipyard for a dedicated size 1 sensor frigate. Expanded the 10kton command ship to 12ktons. Created a shipyard at 16ktons for FAC carriers once jumpdrives got good enough (expanded the commercial yard for jumpships to 16ktons)
Tankers, satellites and tugs get one commercial shipyard. Freighters, colony ships and terraformers get another shipyard. Jumpgate construction and whatever huge thing gets another one.
Now I also have a laser frigate 6kton naval shipyard, 10kton destroyer shipyard, 16kton light cruiser shipyard, with plans to add another 10kton escort destroyer shipyard as population permits.
Plans: Once I have my second industrial planet down somewhere else (ie. at population 2.5billion or so), I will build a new series of shipyards for that planet and have my capital + new industry planet start looking in different directions, as well as split the fleet.
But that's all some 20 to 30 years down the line.