(1) I play on gigantic maps so my ship building revolves around the speed/range of my ships and their purpose. I build fast long range freighters/constructors, or in some cases shells (i.e. ships with no trading or constructor modules, but lots of engines). When the shell ship gets to the intended destination I upgrade it to one without engines of the same range with the trading or constructor module intact. This allows you to send a faster ship with lots of engines where the trading or constructor modules would normally be.
(2) Remember to match the speeds/ranges of your transports to their protector vessels so they move at the same speed.
(3) Warship building is matching your capabilities against the likely opponents. Obviously, location specific ships do not need engines or life support systems so you can use that space for more weapons and defenses. Attack craft come in many flavors and should be mixed and matched accordingly. I use tiny and small ships as attack only with weapons and no defenses. Mediums are my usual first attacker for taking planets so early game they are attack only and mid-late they have a minimal level of defenses. Large and massive ships have robust attack and defense numbers and form the backbone of my attack craft depending on the stage of the game (mid or late game). Tiny and small ships are throw-aways in battle and sometimes absorb the first round hits. This leaves the real attack craft (mediums and larger) a free round of attack to take out the most lethal opponents.
(4) If you played a few games you probably have some ship designs that are usable based upon the tech levels of their components. This allows planning of research and resources to take the research and instantly apply it to your fleet. For example, let's say I have an attack fleet with 8 warships and 5 transports. I can send all of them to their destination while I am working on researching a better level of attack components. You time it so that before the attack fleet moves into the enemies space you can upgrade the warships accordingly, saving you the travel time of getting the research completed, upgrading, then sending the ships. One caveat is if you are at war upgrade half of the warship fleet as individual vessels and leave the non-upgraded ships in a fleet together by themselves. This will protect the upgrading ships for the 1-3 week time it takes to upgrade (with 1 hp). Then repeat with the upgraded ships protecting the individual upgrading ones.
Lots more stuff but this should suffice for awhile.