What kind of interstellar trips are you talking about?
Would this be something like you'd see on 2300's version of Top Gear or maybe a university project to determine how you could make interstellar trips with the minimum of equipment (eg; with special circumstances just to get from A --> B for publicity)? Or do you mean the cheapest ship you could use for transporting people between star systems?
Publicity Stunt: I think the idea would basically be power plant, someone in a spacesuit with additional life support supplies for the duration of the trip, a pre-programmed flight computer for the trip, and the stutterwarp.
Cheapest Practical Ship:
My list (and yes, most are quite obvious):
stutterwarp drive
some type of power plant (theoretically, batteries might be sufficient)
bridge or control cabin
standard navigation sensors
model 3+ computer
stateroom (enough to berth at least half the crew)
Anything else?
Communications - so they can talk to other ships and ground control.
IFF - the ID of the ship that would use the Communications array to communicate its identity to other ships and ground control as well as negotiate the bondafides of other parties to the crew of the ship. Likely it'd be included as part of "computer" and would need "communications" to work.
Pressure hull - should include radiation shielding.
Microcollision Defense - this might be 'plasma shields' or some similar EM field to deflect them away, physical armor (such as whippet shields), or likely some combination of the two.
Standard Navigation Sensors - I'm assuming this includes things such as telescopes, radar, ladar, and whatever else they as sensors in 2300. Must be good enough to detect objects too large to be safely stopped by the microcollision defense.
Life Support - This is actually a much greater mass and weight than many think. It's going to require heaters and radiators to bleed off waste heat (depending). Atmospheric Life Support would need some sort of oxygen regenerator system, a carbon dioxide scrubber, filters to remove odors, either filters and/or sensors to detect harmful gasses, humidifiers and dehumidifers, and perhaps most of all ventilation such as fans to simply make sure the air gets pushed around. Then you'd likely need some sort of solution for toilets (waste elimination) - if you're going for super bare-bones perhaps that might just be equivalent of chemical toilets and if the trips are short and start and end at a starport, perhaps there are no showers so water (liquids) would only be needed for drinking. Otherwise, you'd need a plumbing system and showers, water reclamation (wastewater storage, filtering, purifying, and potable water storage).