About 3/5 of the speed changes needed to get to the Moon have to be acquired just to get to orbit around Earth. So, unless you make that part cheap and reliable, getting to the Moon (or any place beyond Earth) is always going to be extremely expensive. Completely reusable rockets are absolutely necessary for settlement of space. If SpaceX had not already demonstrated that we are close to that day, this project would have little relevance. It's also generally agreed that fuel depots in orbit are necessary. This is addressed early in the timeline using water ice mined from the lunar north pole to provide liquid hydrogen and oxygen (hydrolox) fuel at a new space staion in low Earth orbit. Several investigators have contemplated such an architecture. The work of Paul Spudis and Dennis Wingo are fine examples. The ultimate dream is a space elevator that a car can simply climb up and reach space. We instead have chosen vertical skyhooks for this - giant cables that hang in orbit but don't reach the atmosphere. When everything is considered, they have advantages over a space elevator that make them the better option even once we have materials strong enough for an elevator.
After you get to Earth orbit, getting safely to the Moon's surface involves a speed change of around 6 km/s, which is 21,600 km/h or 13,400 mph. The last part of that involves braking from a speed of close to 2 km/s (4500 mph) to a speed close enough to zero when you reach the lunar surface for a safe landing. Transport in space is a really big deal.
All the ships in this list are self-piloting and designed to work with no human crew, including docking and any emergency avoidance maneuvers that might be necessary. When they carry people, the people are accommodated in modules attached onto the ship for that purpose. In most cases, those modules are easily attached and removed, because most traffic is cargo or robotic missions and there is no reason to haul the extra mass of life support systems and radiation shielding if no people are aboard, it's a waste of fuel. Later in the timeline, some ships specialize in human transport and are are permanently fitted with living space for that.
The question of transport is where it is really striking how much our capabilities would change if we made a serious commitment. Mining ice for fuel depots and building skyhooks is very expensive at the beginning, but they are cheap once traffic is high. The question is whether there is enough to do in space that traffic will indeed explode. The virtual colonies will demonstrate that there is.
These were mentioned above in the Power section. The kind of nuclear ship that could make a big difference, and wouldn't be very hard to produce as we already had a working prototype in the 60s, is a ship that would be used only in space, preferably beyond Earth orbit. Launching a ship like that presents absolutely no radiation risk. The fuel is not more radioactive than rocks until you start to burn it, and since it is only for use in space, you simply don't turn the engines on until you are safely away from Earth. If this was commonly understood half a century ago, we'd be living in a completely different world.
Nuclear thermal ships could attain a specific impulse of 900 to 1000 seconds if we rebuilt that 1960s technology. That's a measure of propellant efficiency. Another way of saying it is that a nuclear engine could heat its fuel so hot it would be moving at 9000 to 10 000 m/s when it exited the rocket nozzles. That speed is what determines how hard the rocket is pushed in the opposite direction by that exhaust. The best chemical rockets have exhaust velocities of 4400 m/s in space - ones burning hydrogen with oxygen. A nuclear engine would speed up or slow down a ship twice as fast as if the ship had a hydrolox engine with the same thrust.
The first lunar missions use Lunar Nuclear Craft (LNCs, pronounced 'links') between the lunar surface and lunar orbit. That involves about 4 km/s of delta V for a round trip before the skyhook is set up. Cargo ships coming to lunar orbit can have larger payloads by handing off their cargo to the shuttle and staying in orbit. The LNCs achieve better performance overall by using a LANTR design. They get thrust by superheating hydrogen, and during launch and landing, can greatly augment that thrust by injecting oxygen into the engine nozzle, basically like an afterburner. A recently developed version of this technology is the Triton engine from Pratt & Whitney. It uses a closed Brayton cycle to also use the reactor as a power source.
The LNCs use a cluster of seven such engines to maximize flexibility and reliability. During early missions, when the LNC is landed the entire reactor assembly, including the power generators, has to be dismounted and lowered into a shaft so the neutron and gamma radiation doesn't affect the surrounding base. The structures of the base are nearby, and the LNCs are used for comms, power, power distribution, and even as a simple crane, with their robotic arm. When a LNC prepares for launch, its engine assembly is raised again and remounted. The LNCs are designed for vertical landing and takeoff.
A good explanation of how nuclear thermal rocket engines work is on our tech page.
Ion engines have now been used to take probes to several asteroids. These engines use their fuel only a very little at a time. The way they shape electric fields to accelerate a stream of ions means they can act only on a miniscule amount of fuel at a time. Though the ions leave at extreme speed, and so gram for gram they provide much more thrust than fuel in chemical rockets, the ion stream is so small today's ion engines provide less thrust than could be provided by a determined bumble bee. That's not an exaggeration. But, they will fire continuously for months, and in the end they will accelerate a spacecraft much more for each gram of fuel than any other engine in use.
That could make them good for getting a cargo ship from low Earth orbit to lunar orbit. The mass saved because less fuel is needed means a much bigger payload can be delivered. Not quite as much as the difference in Isp suggests - the slow, spiraling trajectories used by low-thrust motors take a bit more fuel because they spend far more time breaking away from the pull of gravity near a world. But the portion of a spacecraft that is payload is still several times more than chemical rockets, or even nuclear rockets, can deliver.
However, it would take roughly 6 months for a cargo ship to reach the Moon from Earth orbit, and that could be a damaging bottleneck for the overall project. The early missions are primarily to test prototype robots. Once that test data from the lunar surface is in, engineering teams would have about 2 months before the ship is back and ready for a new payload. (The return trip is faster because it takes less delta V to break orbit, and the ship is much lighter.) Then the engineering teams would have to wait a further 6 months for the new versions to be tested, and again have 2 months to redesign the prototypes and build them so they are ready when the ship gets back. The engineers would either be sitting on their hands or racing to complete new iterations. Since there will be at least one crewed mission in support of all that testing, which couldn't possibly spend six months getting to the Moon, there will also necessarily be at least one large mission using conventional hydrolox (burning hydrogen and oxygen) upper stage engines. So, the cargo ship might as well have next-generation hydrolox engines. After the first tether orbiting the Moon is complete, there would be no further role for an ion-drive ship on the Earth-Moon run, anyway.
For launching from the Moon to deep space destinations like Mars or Venus, low-thrust ion drives could be a good choice. NEXT ion drives require a tenth of the fuel of hydrolox engines for the same delta v, a HiPEP ion drive about a fifteenth (that one is still in development though).
Neumann drives would be even better if they are successfully developed. They employ micro-second pulses of electric arcs to create tiny puffs of super-hot plasma on the surface of a disk of fuel. The hot cloud of atoms expand into the vacuum of space, resulting in them pushing the rocket in the opposite direction. They look promising as long as no issues show up during on-orbit testing of a working model, which should happen in 2018 on board the ISS. They might be available in a decade or less. They could be fueled with magnesium sourced from the Moon, or aluminum collected from scrapped satellites and spent upper stages, or even carbon from the waste produced by a human crew.
The VASIMR drive by Ad Astra is another promising candidate. It too is ready to be tested in space. It uses shaped radio waves to create ions and super-heat them into a plasma that is then magnetically confined so it leaves the nozzle as a narrow jet. It can burn hydrogen, argon, or xenon, and can vary its thrust, unlike the other options.
Each of these systems have their pros and cons, and different situations can favor one over the other. To push large vessels, all of them require the development of big power systems capable of feeding the engines energy at a very high rate. They all need giant solar panel wings, for missions that don't go farther than about the orbit of Mars, and nuclear power plants for missions further out.
These drives come into play in the timeline when asteroid retrieval begins. The Fetcher ships use them.
The pod ships are so named because they haul shipping pods, which are the space equivalent of shipping containers on Earth. They are manufactured in a standard size, with standard specifications for insulation, Whipple shielding (for protection from micrometeoroids), a sliding door, internal structures for storage, and connectors if items need power or a comms connection. Eventually these pods are mass-produced.
The initial pod ships have space for 8 short pods or 4 long ones. The pods are attached to the racks on the truss that forms the spine of the pod ship. The nose of the ship has all the ship's systems, a robotic arm, wings of solar panels, and radiator panels. The far end has the fuel tanks and engines. As the timeline proceeds they become ever larger and beefier. Eventually they are phased out when toss ships take over shipping, except for routes between space stations or other facilities that aren't close to a skyhook.
The pod ships are assembled in orbit at the timeline's beginning, allowing them to have this shape, and be large enough to haul substantial loads to the Moon. They are not equipped to land anywhere, they are strictly in-space vehicles. They burn hydrogen fuel with oxygen in ordinary chemical engines, so they can be fueled with the water mined on the Moon. They could instead be fitted with nuclear thermal engines like the LNCs, the question would be whether the possibility of a pod ship crash is so remote there is no need to think about a nuclear reactor breaking up on entry to Earth's atmosphere, or about managing radiation when the engines are firing close to the space station in low Earth orbit. The immediate construction of the first skyhook perhaps argues in favor of being conservative and avoiding the use of nuclear reactors near Earth and its space station. Once the skyhook is operational, little fuel is spent getting a fuel payload to lunar orbit, and the pod ships can break lunar orbit on a good trajectory to Earth without spending any fuel at all. The need to pare down fuel use as much as possible thus becomes much less important.
When people travel on the pod ships, they do so in habitat pods specially adapted for that. When they arrive at a skyhook or are transferred to another ship, they don't leave the pod. The whole pod is instead disconnected from the pod ship and its robotic arm places it on the skyhook climber or in a rack space on the other ship. This means that the pod ship rarely has to dock in the precise manner ships today must do when arriving at the ISS, it just needs to berth in a space very analogous to a berth for a boat on Earth. Early habitat pods have airlocks which must be mated to a receiving airlock when the people aboard are arriving or departing a destination. Later on, hab pods are received in bays that then are sealed and pressurized with the entire pod inside.
There are several other ships documented in the Timeline - Toss Ships, Fetchers, Hoppers, Schooners, Galleons. In the interest of advancing with modelling of the colonies, these ships will be left for later. Material on them will be posted after their models are done and placed in a much improved virtual colony.