LazerBreath Cosmoteer really is a balancing act when it comes to firepower, speed, defense, versatility, and cost. Every design does indeed have its strengths and weaknesses.
I'd recomend going over to the Building Academy Thread: https://forum.cosmoteer.net/d/8610-building-academy/607
The other actual teachers (AKA, not me) would probably be able to give you better pointers if you post some ships over there!
And feel free to take aspects from my designs. I mean, I'd like some credit, so as long as you don't claim ownership of 'em, we're all good 🙂
Here's another design I've got, if you'd like to see. I have some more posted around in that thread I linked (you'll have to scroll a bunch, though).

EDIT: Yeah carriers aren't generally considered "competitive", at least not in the traditonal sense of a carrier, in which you have a large mothership that holds fighters. Swarmers, which are really just a bunch of connected fighters without a central ship that then split when the battle starts are more common, and can work well.
Even still, I love carriers anyways, so 😉