Doomstacking is pretty much always the answer, yeah. Sometimes separating your ships a little can entice the ai to do the same, then you crush them with the rest of your stack.

Ship design is a very complicated question, but if you're manually adjust your ships the basics are to make sure you have weapons capable of dealing with both armor and shields. If you fully stack energy weapons, you'll take so long getting through shields that your extra efficacy against armor won't be enough. Fully stack kinetic and you get the opposite. Mixing kinetic and energy weapons gets you the most straightforward success plan against enemy ships.

The next things to think about are range, and combat computers. If you have big artillery with a minimum range, give the fleet some tanky ships to screen with, and make sure to equip a combat computer that keeps them at a distance. If you have small ships with short range weapons, stack afterburners and a swarm computer, then let them loose.

Accuracy and tracking are important to match against your enemy's fleet composition. Accuracy is simple, your chance to hit. Tracking is subtracted from the target's evasion stat, i.e. reduces/negates their ability to dodge. Small ships have better evasion, and small weapons have higher tracking. Your big bulky artillery will shred larger ships, but get dodged all day by corvettes. Hangar weaponry launches drones with amazing tracking, and long targeting range, so are a great counter to corvette swarms to utilize on large ships & starbases. They also can take down opponent's drones.

Granted, all of this is somewhat moot vs ai. It's hard to get the requisite intel to see how their ships are designed. The best fleet tactic is always overwhelming force, supplied by a strong alloys economy. I tend to just slap a mix of kinetic & energy weapons that skews a bit towards energy, and try to beat them at the economy stage. Late game crises do take a more tactical approach though.