I don't think your proposal is practical. The "space pickup truck" idea is nice, but the idea that it should descend to and lift off from a planetary mass is unfeasible, without controlled fusion, and perhaps even then. (You could do something similar with some sort of skyhook [the PinWheel is my favorite, as being the most practical in the near term].)
But FIRST you need to work on a nearly-closed eco-system. This "space pickup truck" will take a long time to make a long trip. It will probably be powered by solar cells and a ion-jet of sorme variety. This will let it move from orbit to orbit, carry things along, etc., even do interplanetary voyages. But it's SLOW. This means that it needs to be either robotic or a closed eco-systme. (Well, nearly closed. Really closed is impossible.) And if the people who are inhabiting it are going to remain sane, it needs to be large enough to live in. Larger, probably, than a hutment in Antarctica. (It's easier to go outside in Antarctica, and less expensive of habitability. In Antarctica that just means heat, in space it primarily means air and water...no matter how careful you are.) Also, if you design it for habitability you need to carry along significan radiation shielding. Water is probably a good choice for that. But that means weight.
If, OTOH, you only mean short interorbit transitions you still end up with a slow vehicle. And one that can't land on a planetary surface.
Please note that the same driver frame should be able to have several different cabins mounted on it, and should be able to haul cargo. But that's really tricky when you're using rocket/jet propulsion. You can't haul the stuff behind on a cable, unless it's WAY behind, and then the cable had better be able to stand being exposed to the wash of the exhaust. Probably better would be to have three or four main engines angled slightly outwards, and slightly manuverable, to allow hauling things on a cable, even though that would reduce the efficiency. But adjustable, so if you weren't hauling cargo you could eject straight backwards.
Please note that this approach won't work much beyond the orbit of Jupiter, as solar cells will become too weak to generate enough power. So you need some alternate power source. Fission reactors are the only thing that currently seems feasible. Fission reactors are probably enough to allow manuvering throughout the solar system, but for interstellar, even at slow speed, fusion may well be needed. (I suppose that one could build an anti-matter factory near the sun and power it off sunlight, and then store it as fuel...that seems only an engineering problem, with no theoretica breakthroughs required. But it's a HUGE engineering problem.)
Near term, though, to get from a planetary surface with an atmosphere, use a skyhook. (Some could be built now. They aren't all as difficult as an elevator.) If there's no atmosphere, use a catapult. Ion rockets to get from orbit to orbit. And human presence requires a nearly closed ecology. Which can be developed right down here. Siberia or Canada seem like good locales to do the development, with other locations if it needs to deal with excess heat rather than excess cold. (And note that right now the real requirement is cheap land that can be somewhat isolated, and funding. BioSphere & BioSphere II were examples of attempts that have failed, and in failing taught us something. But nobody's put serious effort into the development. And it needs to be done before anyone does any serious planning about a permanent human presence off the planet.