The AI at lower levels cant beat capital ships so if you lead them in the middle of his fleet to be able to fire in all possible directions it's good, just retreat them if they are being heavily attacked. Same for antifighters and illuminator vessels, but one of them will not require to be retreated . Capital ship abilities require micromanagement, so if you can hurt many ships with an ability try maximize its effect, not waste antimatter with autocast and hurt only his capitalship or something. AI likes to build capital ships even if its of no use, it worked for me to kill them in high priority, same for titans, this way ai loses extreme amount of resources, while you lose only little. Same goes for counter, don't let your ships go in the middle of ai fleet where everything can attack them (like light frigates going in the middle of his illuminator fleet), dont let your ships stray too far from where they are wanted, they waste much time by chasing one ship and meanwhile they wont attack anything. Positioning means much, you can kill an equal large AI fleet easily while he has a starbase just by not going near it. Early game its even more important to kill ships faster, so like not letting your corvettes attack light frigates, instead attack long range. same goes for all ships, they are better off attacking ships they counter well.

Defending against high level AIs: if you build a starbase and many defense structures next to it (but in range), lure AI into range thus starbase can shoot at it while that dumb is chasing your ships, taking heavy losses. Its the best to have his fleet completely surround starbase, thus it can shoot with all weapons. He even let his capitalships die while not standing a real chance against your defense. Once i could kill 6-7 high level Vasari capital ships with a small support fleet with only beam platforms shielding themselves and some repair, and hangar to give more shields. He didnt realize he should retreat, losing 8 turrets are nowhere as big loss as losing 6-7 high level capitalships.

I recommend reading the table of attack %s, what ships do what amount of damage against other type of ships, damage type I think. This way you will know with what ships who to attack with, and what is the best way to counter something.

Watching replays of online matches are good to learn many things, but AI won't be as clever as a human, so maybe not everything will be useful against it. Honestly I don't know, after I got to play Multiplayer a month ago I never played single player again, but before it I only played single for years.

https://www.sinsofasolarempire.wikia.com/wiki/Counters

There is also the issue of anti-structure frigates, which will quickly pound your fixed defenses into scrap if your fleet is not actively seeking them out and neutralizing them. Even though they are fragile, a large group of these ships (especially the  Adjudicators, which target multiple structures simultaneously), can do a tremendous amount of damage in a short period of time while you are picking them off.

Everything changes once you are up against cruel or vicious AI bit  not much really. most of the time (early game) you can just run your capital in circles around your SB turrets and repair platforms. AI will simply folow it and try to destroy capital ship first. He will be suiciding his fleet wave after wave and level your capitals. If he does manage to seriously dammage it just warp another one in and damaged one out.

Rinse and repeat.....

Things do change a bit with adjuncators but not too much. for them you just need to sacrifice certain amount of corvettes or be fighter heavy.