'Ship' is out of fashion as a term for spacecraft; 'spacecraft', 'vessel', and 'space vehicle' are preferred. The most ardent exponent of this nomenclature is the USAF, adamant that 'ships' are what the U.S. Navy operates.
New spacecraft often cost $100 million or more. A few individuals or partnerships own one, but corporations or governments own most of them. However, even in company-owned craft, a crew might be assigned to a particular vessel and stay with it for several years, only gradually changing in composition as individuals leave and new members are reassigned or hired.
Most spacecraft are propelled by reaction drives. They work on the Newtonian principle that for every action, there is an equal and opposite reaction. A drive throws reaction mass, usually heated to give it extra energy, in one direction, and the reaction accelerates the spacecraft in the opposite direction. On a long voyage, a vessel will accelerate for several hours until it has used up around half of its reserve of reaction mass, then coast at whatever speed it has achieved for several days, and finally spend the other half of its reaction mass to slow down.
Most modern interplanetary spacecraft use fusion drives, which accelerate slowly but are efficient enough that a vessel can achieve a high speed over many hours without running out of reaction mass. Fusion drives lack sufficient thrust to overcome the gravity of a decent-size planet or moon, so these deep-space vessels park in orbit and use craft with higher-thrust but shorter-endurance chemical or fission rocket engines to shuttle to and from the surface.
Interplanetary trips typically take a couple of weeks in the inner solar system, or a few months to cross the outer system. Spacecraft are large - hundreds of feet long - but crews are quite small: 2-12 people is typical. Large passenger vessels have rotating sections to provide spin gravity, but most other spacecraft are in zero gravity for the majority of the trip. Crews are zero-G-adapted parahumans, or have nanosymbionts to keep them in good health; passengers take temp nanomods, exercise rigorously, or shut down their metabolisms altogether and spend the trip carried as cargo in nanostasis.
Space crews are busiest at the start and end of a voyage, when the drive is hot and they're near a port bustling with traffic and surrounded by space junk. In deep space, with the drive cold and the vessel coasting, there's less to do. Routine maintenance is usually handled by microbots or cybershells.
Light-lag means they cannot access the Web at real-time speeds, but slinkies, entertainment, mail, etc. can be downloaded. Crews take up hobbies or study, and war crews run battle simulations. A pet, often uplifted, is not uncommon. Some vessels are loose about intracrew relationships, handling any difficulties informally. Others, mostly big companies and the military, have strict 'no fraternization' rules (but some crews acquire pleasure bioroids, bioshells, or cyberdolls.) A few vessels are family-operated, especially Gypsy Angel craft.