Several shows provide the inspiration for that!
The ship has a female avatar that appears onscreen, as well as in a manufactured humanoid body, affectionately called "Rommie", which allows players to interact with the ship and shout commands to it, while it speaks and expositizes to them.
This high level of technology handwaves the need for a lot of repairs and refitting and resupply (unless it's a plot point for the episode), and rationalizes why such a small crew can pilot the damn thing. It also allows players to skip having to answer to a rigid chain of command and go 'adventuring' in pursuit of their goal.
The alien nature of the ship allows them some tension that Andromeda lacks when on the ship -- except when something happens to Rommie, of course -- because the crew struggles to control it and are forced to interact with Zen when it refuses to do exactly what they say.
Also, the speed of the ship allows them to criss-cross a vast interstellar empire and carry out their little missions of rebellion and revenge.
Once again, there is potential for tension due to the alien nature of the ship and its Pilot, as well as the sense that the ship is alien and isn't entirely understandable in the way that an inanimate ship built by one's own race might be.
Moya had no weapons, by the way, except for the defensive capability to Starburst (jump through a tear in space and time) to other locations. This made it interesting when other ships tracked them and shot at them.
Talyn, another Leviathan and child of Moya, had weapons -- but was more of a genetic experiment on the race of Leviathans that escaped.
Next: examples of larger ships that follow the 'aircraft carrier' role in a campaign.