I'm trying to find out how to design ships effectively, but I can't find any info, i.e. how I should outfit my battleships to be most effective, ratios of defense to offense, support modules, etc.
Any links or advice?
Try military books on ships.
Unfortunately, I can't recommend any because I haven't actually read any.
Edit: I thought this was a general question, sorry.
Just try out different things. Ship construction, like pretty much everything else in that game, really is a learn by doing exercise. Specifically which exact load out will vary depending on you and your style of play.
A little helpful advice though, try and split them off into four categories. Capital fleet, huge ships loaded out to stay in orbit of important systems and blow anything that tries to take them to hell. Response fleet, fast groups that can be mobilised and deployed in a hurry, made up of lots of smaller ships rather than a few large ones. Invasion fleet, halfway between response and capital, also carrying some serious planetary ordinance (only necessary if you're planning to do some planet twocing). Emergency fleet, small ships requiring very little resources or dust that can be built on a planet under siege to hold out until the response fleets arrive.
Also, keep changing things up, if you use the same loadout for a while the enemy will start building ships to counter that. Bear in mind they'll be doing the same.