Trinity is the equivalent of the Diplomacy expansion, and has all the features of Sins enabled. Picking a chapter allows you to go back say just the Entrenchment expansion (without the diplomacy enhancements) or even original sins, without either expansion. This can be useful if you want to play a mod not for Diplomacy or you have some friends who don't have trinity but have the original or Entrenchment.
There is some debate as to the best way to learn the game. If you have time to spend really learning this game I would start with the original sins until you can beat a normal or even hard AI, as it really teaches you fleet management without those powerful starbases to defend yourself with. After that play a game or two of Entrenchment to get a feel for the new features and then finally trinity/diplomacy. If you just want to get over the learning curve as fast as possible, start with trinity. The first option will make you a better player, the second will allow you to get up to speed as a decent player faster.
As for Bailknight's mod, the link in the original thread is out of date for Diplomacy, but the one for Entrenchment works fine. The community has unofficially updated it for Diplomacy 1.32 as well, the download link is in the last few posts of the thread instead of the OP though.
Further, I advise that the Devs add custom map sharing to Sins of a Solar Empire: Rebellion.
