I can see a clear path to progressing toward colonies and the current "endgame" content, but I'm completely overwhelmed by the ship system. I get that it's the heart and soul of the game, and deserves a lot of depth, but the sheer number of ships/weapons/etc. are really leaving me feeling stuck and not knowing how to tackle the whole thing. I tried piloting a few ships myself and it was way harder than I expected it to be. I guess this is good, that it's no so easy that it's boring, but I quickly reverted to just zerging other fleets and letting the AI pilots work it all out, which leaves me feeling a little disappointed.
I felt the same way when I first started, so you're not alone. What helped me was to come up with a "theory of victory" for each ship I outfitted. Ask yourself: how will this ship kill the enemy?
To kill an enemy ship, you need to do three things. First, build up flux on its shield until it drops shields or overloads. Second, you have to break through its armor, and thirdly, do enough damage to its hull to destroy it.
Low-tech ships will typically use specialized weapons: kinetic weapons to deal hard flux to shields, and high-explosive weapons to break armor. Once that's done, the combination of the two should be enough to finish off the hull.
High-tech ships will typically use more generalized energy weapons for all three. Midline ships are a little more complex - they use ballistics too, but also energy weapons that are typically long-range support beams. Missiles and fighters can also be used to supplement your capabilities in each area - pay close attention to their damage types.
One other big thing to be aware of is the tradeoff between speed and range. Slower ships will have longer ranged guns to make up for their pokiness, and quicker ships typically want to mount shorter-ranged (but more powerful) guns and do hit-and-run attacks. It's often a good idea to make fast ships faster and long-ranged ships even longer-ranged (always add Integrated Targeting Unit to cruisers and capitals).