By carrier I mean people This is in the distant future so we can ignore the materials and the time it would take to make it. Lets just say the government have the required materials to make it.
The ship is designed with the survivability of the people in mind
It will hold 10k. Aside from the crew (5) all the others are held in cryostasis.
The reason a carrier has weapons in the first place is it's a solo ride, they can't refuel, and can't receive any help against danger. Even if they could get in touch with another carrier. Warp drive wasn't put on this ship. So unless they are right next to each other they are one their own.
I'll give an estimate on how I think the spacing would work: People 45% Defensive 25% Offensive 5% Life support and entertainment 15% Nav and comms 10%
The offensive system is mainly used to clear debris but can double as a weapon.
The reason I didn't specify fuel is because they have none. They used most of it during launch. They are free floating in space and can only use the fuel leftover to make minor adjustments to not crash. Their Nav systems are advanced enough to see obstructions from a good distance and change course.
To answer two questions at once interplanetary vs interstellar and time frame. All I can say is that it would take awhile to find a suitable planet. Especially one with Earth-like conditions. I'd say Interstellar And with 10K people being on board. Despite cannibalism being morally wrong they technically have an abundance of food. So they can spend a long time in space
The debris I mentioned before that would need to be cleared are mainly asteroids in the way since the don't have fuel to avoid them.