As is common in EVE lore, info is generally scattered around here and there.
My advice would be to search “weapons” in the fiction portal. Many results seem to be about ground weapons, but for example one result is the chronicle “war drones on” which explains a bit how Gallente came to rely on drones in warfare, dating back to time when only Caldari had the pod technology, before it was spread between empires.
@Bjorn_Tyrson did give a fairly good overview for preferences IMO, Amarr definetly like the “divine wrath of God’s light” aspect of lasers, Gallente historically have less volunteers for military so automation is essential to reduce manpower needs, though they are also in your face with extremely powerful blaster weaponry, backed up with advanced armor repair systems. Caldari similarly prefer to avoid loss of life and love efficiency - long range weapons are preferred, and hitting hard.
It is a common misconception that Minmatar technology and weaponry is inferior, but you try to launch shells the size of a bus (Naglfar’s projectiles are 2.5m or 3.5m in diameter) and tell me its simple. Not to mention that the shells have exotic payloads like phased plasma, and advanced versions can adjust trajectory after exiting the barrel. Additionally, I believe Minmatar value the reliability of “lesser” technology. Why use bleeding edge technology if just nuking them works just as well?