I've managed to beat this mod on deity, mostly because the AI is not very good at combat (they build mostly battleships and some destroyers). So here are some of my tips:
Each of the civs plays somewhat differently. I like Hector Alvarez of New Earth for expanding quickly, or Lukas von Reuther of the Brotherhood for fighting.
One of the first techs you want is Light Craft Manufacturing because that lets you use the Monarchy government, which is a big boost to your capital.
My favorite unit is the bomber squadron. They're good for defense because they can instantly rebase anywhere in your empire to fight incoming threats. You can pretty much ignore the military techs in the top row of the tech tree for a long time, because new bombers and planetary defense ships are in the builder techs. Those two ships are enough for a tough defense. Bombers are also good for bombing enemy stacks and planet defenders with little risk to themselves. But you'll need to move them on carriers for that.
Make sure you grab happiness and health resources early on by building starbases.
Look for big planets in the systems you colonize. That way you have to build fewer mines, nutrition facilities, and things like that. You can build multiple copies of most buildings, but each copy costs more than the last, so avoid it it you can. The planetary development is complicated, and it's the thing most different from unmodded Civ 4.
My favorite values are Wealth for financing planet maintenance, and Power for building elite, customized ships.
An important tech in the middle of the game is Terrestrial Networking, which lets you build Commercial Satellites. Those give you a big boost to commerce.