Commonly in science fiction you'll find two main modes of interstellar travel. In the first, common to several well-known franchises on the big screen, ships are plentiful and swift, crossing between star systems within the attention span of the average theater-goer. It seems like everyone has an interstellar craft, as small as two-seater runabouts and small fighters. In the second, less common, model, ships are still limited to sub-light speeds and journeys require lifetimes, either using multi-generation ships or sleepers. In this genre there is virtually no interstellar commerce because it takes too long to be practical.
For this story, I wanted interstellar commerce to be possible, but rare and slow, much like the earlier days of sailing vessels on the seas. I also wanted a mechanism with a firmer scientific foundation than hyperspace and wormholes. The theories of Miguel Alcubierre and the extensions by Harold White of NASA fit well into the sort of interstellar drive that just might be possible. Such a drive would contract space before the ship and stretch it out behind so that the ship would appear to move faster than light without accelerating in its own frame of reference.
Such a ship would require a negative energy field, is a property of exotic matter that has been postulated but never observed. In my economic model of this universe, I assumed that such matter could be manufactured, but was extremely rare and expensive, and would require large and powerful containment fields. Practical starships would be large vessels, and humanity could only afford to make a small fleet. I put that number at around eighty vessels serving five hundred settled worlds; a starship arrival would be a rare and exciting event.
Let's further assume that the top effective speed of such a ship was one hundred times the speed of light in the frame of reference of the local star group. Seems plenty fast, doesn't it? It would still take two weeks to journey to the very closest star, and six weeks to travel to the nearest star that is currently thought to have planets that could support life. Interstellar voyages would take months. In this universe, I staked out a sphere about 200 light-years in diameter that humanity had explored. That's a tiny corner of the 100,000 light-years our galaxy spans, or the 3,500 light-year cross-section of the local arm. Our mighty starship would take two years to cross human space, 35 years to cross the galactic arm, and over 1000 years to cross the galaxy. Space is vast.
I assumed that it would take exponentially more bottled up exotic matter to create a deeper warp field. The deeper the warp field, the faster the apparent velocity of the ship. To double the apparent velocity would require eight times as much exotic matter. A small ship would only be able to carry enough exotic matter to achieve slightly more than the speed of light. That's not very practical, since a round trip to the nearest star would still take eight years. On the high end, large ships would become impractical as the mass of the exotic matter and the size of the containment vessel outstripped the cargo and passenger space inside. This places an upper limit of around 100C on the speed of starships, and also imposes a maximum size on them (so you can’t use this drive to move moons around. Sorry, Darth). The largest starships would be comparable to an ocean liner in size.
A starship under warp drive is protected from interstellar debris by the cone of wrinkled space projected in front of the ship. All that debris accumulates as a bow wave of hyperluminal particles riding in front of the ship. Once the ship drops the warp drive, that debris suddenly gets an interstellar speeding ticket and flashes into Cherenkov radiation and hard gamma radiation. Consequently, any starship entering a star system is also a weapon. Captains take great pains to be pointed well away from inhabited planets when dropping out of warp. Standard procedure is to come to rest outside the plane of the ecliptic, then to move under subluminal warp to within planetary distance, then to complete matching orbits under ion drive. Since Cherenkov radiation has a characteristic blue glow, that is the genesis of the "blue sword" seen when a starship arrives in a system.