Here’s my issue: What is the best type of propulsion to use for such a trip?
Depends on your timeframe, but there are some esteemed propulsion engineers (one or two with whom I've worked) who believe that within one hundred years we will have developed and refined existing electric propulsion technology to the point where we could achieve delta velocities of around ∆40km/s. This would allow spacecraft to travel to Mars in 2 months, Saturn in 1.8 years, Neptune in 6.4 years and the very edge of the Solar System well within a lifetime. At these speeds it would take around 22 years to travel 100 Astronomical Units (AU). However, this doesn't really solve the problem of interstellar travel, considering that Alpha Centuari is something like 250,000 AU away.
But the technology could be pushed, in theory, to generate vastly increased velocities, potentially up to 154km/s.
So how does it work? Electric propulsion uses three main components: a thruster, propellant, and a power supply. Your thruster, powered by the power supply, fires the propellant particles into a chamber where they are ionised, creating a neutral plasma. This plasma is then accelerated in one of two or three different ways (electrostatic, or separation of electrons and ions and induction of separate electric fields) as a jet through an exhaust. If you remember your Newton's 3rd Law of motion, this thrust acts against the outer environment (in this case, space), and generates thrust. The jet can be accelerated to induce a steady, constant acceleration, and in theory you can reach some very high speeds indeed using this method, at a high efficiency.
The thing about this tech is that it's theoretically scalable, so if you increase the power to accelerate your electrons, you get more thrust. But to generate this sort of power you need a nuclear power supply, which is kinda dangerous (not to mention extremely expensive, although you could theoretically use cheaper Americium as a fuel rather than plutonium - in fact Americium is a byproduct of plutonium processing (I can't remember which isotopes though).
So you don't just need to make a more efficient propulsion system, you need to make the spacecraft itself
into the propulsion system. To do this you could have to create a spacecraft that would be capable of generating its own substantial, superconducting electromagnetic field, and electrical currents running across it in the range of millions of electron-volts, probably using in the region of dozens of Megawatts of power. Alan Bond, who used to work at Reaction Engines, has postulated that such a vehicle would look like a Flying Saucer, which is is pretty cool. The craft would weigh about 15 tonnes, require tungsten shielding, some serious heat rejection / radiator capability to dissipate the heat generated (which would be substantial)
So that's sort of getting there, although strictly speaking is probably not enabling interstellar travel (I've done some back-of-a-fag-packet sums, and I reckon it'd still take, er, 8,400 years to reach Alpha Centauri using the upper performance levels of this capability). Even so, this represents the limits of what we currently know with existing tech*, and would enable us to get to the very edges of the Solar System (the Oort Cloud etc). Which is still cool.
But - and this is important - you're writing science fiction, so if you just want to convey a realistic piece of futuristic engineering, all you have to do is massage the figures, use a bit of handwavium to get around the nuclear problem and you could pass this off easily as a viable futuristic piece of space propulsion kit in a couple of hundred years' time that could reach Alpha Centauri or wherever.
Of course that's assuming that the various countries of the world can work together sufficiently harmoniously to make it work. Not impossible, as space is one of the few areas where the world does see, to be able to cooperate and collaborate on a global scale. Not that there aren't disagreements. Note the planned Lunar Gateway. But that's a whole other story...
It's worth mentioning that almost all of the "engines" that are depicted in SF are some form of electric propulsion thruster. The Enterprise has an Ion Thruster (not the Warp Drive, which is basically magic
); the Battle Cruiser in Star Wars uses Gridded Ion Engines, and so on.
*Alternatively you could use solar sails, but that is still theoretical tech and I don't know much about that!
ETA: I forgot to mention, for this propulsion method, you will need a propellant that is safe, non-contaminating and inert. Kerosene is not an option here as it's not efficient enough. Really you'd want stuff like Argon, Krypton, Xenon, those sorts of guys who play nice and won't explode when they get irritated. Also, if you land on a planet with water you could use cryogenics to separate it into liquid hydrogen and oxygen, which you could then use as more fuel. So it's a pretty flexible system, too.
