I think the Danube-class would be an excellent choice for a campaign. With the DS9 Tech. Manual as an aid we have a nice resource as to the interior of the ship, and a good understanding of its capabilities and uses.
The class is a courier, which would make for an excellent campaign setting. And with a crew of four it would make for a nice cozy game. The players would fill the roles of CO/Flight Control, OPS/Tactical, Engineer, and Science. One could forgo the Science slot and allow a second Engineer. The CO/Flight Control would, I feel, need to be an officer; while the rest of the crew could be senior enlisted. But then they could all be officers, the most senior being a lieutenant junior grade (or a lieutenant, I wouldn’t go higher than that).
Making courier runs in an assigned sector would allow all kinds of adventures. And with the different modules available (and of different sizes) it opens all kinds of possibilities. One could also have guest appearances, characters acting as payload specialists for each module they are transporting this week: Supply Officer/Specialist [enlisted] for cargo; Science Officer/Specialist for lab modules, ect.
Using the cargo module(s) the crew could be assigned a resupply mission of goods from Starbase 375 to DS9 that cannot wait for a proper freighter to take them, and be accosted by Ferengi in an outdated ship attempting to hijack the cargo. While transporting lab modules to such and such destination racked by a devastating plague they find themselves trying to prevent the limited colony population from fleeing and carrying the disease with them to other worlds (and perhaps have a hand in bringing the plague under control). Using the emergency habitat module the crew could be assigned the planting of a special forces squad on some remote Dominion/Cardassian world. Likewise they could be charged with the retrieval of such a team. With the additional living quarters module they could be tasked with the evacuation of a diplomatic team from a world suddenly gripped by civil unrest. The players could be assigned to pickup the personal module of an ambassador used as a mobile embassy and uncover one of the ambassadors staff selling information to Yridians. After retrieving a set of lab modules the crew is dispatched to a relatively close world though uninhabited, but suddenly broadcasting subspace transmissions.
And there is lots to do not centering around the modules. En route to such and such destination they get sidetracked aiding a vessel in distress. On such and such world they find themselves with some free time, and accidently stumble upon the Ferengi who attempted to hijack their cargo who was able to escape after the attempt failed. They find themselves amidst a fair sized colony trying to track down one being and bring him to justice for piracy. From an adventure I found on-line that I would love to run: the crew, waiting for a cargo module to be filled, explore the exotic downport and fall victim to a juvenile pickpocket. One member of the crew recognizes the child as one reported missing. Now the crew needs to locate the child before the local authorities, or the bounty hunter looking to collect the reward.
I think a runabout campaign would be very exciting, and I would love to run one if ever given the opportunity.