This is probably the best MOO2 strategy guide available on the Internet: [url=https://strategywiki.org/wiki/Master_of_Orion_II:_Battle_at_Antares][/url]
It provides in-depth details of almost every aspect of gameplay, including how damage for various weapons and defensive technologies is calculated. You might be most interested in the section on warship design: [url=https://strategywiki.org/wiki/Master_of_Orion_II:_Battle_at_Antares/Warship_design][/url]
There's some trial and error involved, but it's mostly a matter of knowing how certain game mechanics work, and which technologies can best exploit those mechanics. For example, weapons that are "enveloping" will attack all four sides of a ship simultaneously, damaging all of its shield quadrants at the same time, but will also deal four times as much damage to unshielded targets (like space monsters). The fusion beam, the earliest beam weapon you can research, is one of the weapons that can be given an "enveloping" enhancement, but you'll have to complete a couple of additional levels of research in the physics field (completing the 900 RP tier, with neutron blasters/scanners) in order to unlock it. You can also give fusion beams the "continuous" enhancement, giving them a higher chance to hit, but this will make them take up more space.
There are certain key techs that will give you a big boost to your offense and defense. Having a decent computer or battle scanners is important, as this greatly affects the chance your beam weapons have to hit their target. Reinforced hull triples hull HP, while heavy armor triples armor HP. Neutron blasters kill marines when they inflict damage, which softens up a target for boarding parties using assault shuttles or transporters (and you can then scrap the captured ships to get any technology you haven't researched yourself). Shields are helpful, but don't offer real protection until class III or higher; class I is too weak to be useful. Structural analyzers double all damage that gets past shields. Plasma cannons are naturally enveloping and don't require additional enhancement. Anti-matter torpedoes can also be modified to be enveloping (once you complete the 3500 RP power research tier), which makes them one of the most dangerous weapons in the game, as they take up relatively little space and never run out of ammunition; you can load up a ship with a structural analyzer and nothing but enveloping torpedoes, and watch it wreck everything, including Antarans and the Guardian.
The biggest challenge you'll have is prioritizing which technology to research, as some of it is mutually exclusive, so you won't be able to get everything you want; heavy armor, for example, is in the same research tier as automated factories, which are extremely useful to get your production off the ground in the early game. This may be less of an issue for you playing the Psilons, as they are a Creative race and will eventually get 95% of all tech in the game anyway, so it's more a matter of "turtling" and surviving long enough to develop all the technology you want.
EDIT: Links to the guide are showing up wonky, the URL might be too long for the forum to handle. Just throw 'em into your address bar and they should work fine.
Post edited October 24, 2023 by srhill