This question is far, far too broad as it involves either compressing everything in the manufacturing and technological chain down into a relatively tiny space and then combining it with a power source that can actually run everything.
If you're not going to miniaturize everything we already have, then you're going to need to find equivalents for all of those.
This covers virtually every technology in existence, as well as a very large number of those that don't yet exist.
It involves everything from start to end:
- Mining (surveying, analysis, drilling, digging, smelting, refining,
- Forming (cutting, grinding, lapping, honing, forging, casting,
welding, etching, weaving, growing (crystals))
- Post-treatments (hardening, plating, painting, doping, etc).
- Assembly (actually grasping, moving, and fastening everything
For example, it's not just good enough to have the technology to cut screw threads. You need to be able to cut ANY screw thread on ANY material ANYWHERE. Virtually every technology we have is not good enough as is due to either taking up too much space, requiring too much power, requiring too much stuff, or being too special-purpose.
I know there's talk about 3D printer being able to make "everything", and its true they have the potential to eliminate a lot of other machinery. But even if you assume they have advanced to a point where limitations in workable materials is no longer an issue, there are so many more processes involved in making something just not covered by 3D printers. And 3D printers do nothing for mining and processing of raw materials.
The only example that even comes close is biological organisms, and we all know those succumb to the rigours of space.
The next time you eat an apple, think about what it takes for your body to turn that apple into something that both provides the energy to run your body, and materials with which to build your body with. Then think about what it takes for your body to turn that apple into something that can provide it with energy AND materials to construct itself with. And that's an apple; It's not even the raw material. That apple has been pre-processed by an apple tree into a form that is suitable for your body. Think about what it took for the apple tree to grab sunlight, soil, and air to make that apple. You need that, but better because in space there is no biosphere to support you; You need to be self-sufficient.
Going back to biology, there's a reason biological organisms are mostly made of hydrogen, carbon, oxygen, nitrogen, and phosphorus rather than copper or iron. The former elements are far more abundant and you don't have cover a huge area to find them. Whereas with metals you have to process huge amounts of ore to get enough bulk material to work with. So the initial stages might actually have less metal machinery (other than what you brought with you) and look more like wood, plastics, or carbon fiber which are all made of far more abundant elements. Asteroids do help though with the scarce metals though.
The caveat is that you need to pump energy into those molecular bonds, and unlike a block of iron where you can pump the energy into it rather crudely to smelt it, to form wood or plastic from elemental carbon and hydrogen takes finesse. The question might become whether it is more efficient to search far and wide for metal ore (though asteroids help), then dig down and refine it or whether to use more abundant non-metallic elements in-situ and use energy to very precisely form the bonds to produce a construction material.
There's also the question about whether it takes more energy to smelt and refine a block of iron than it does to pour energy into hydrogen, carbon, oxygen, nitrogen, and phosphorus bonds to form wood or plastic. A wood or plastic fire can't melt iron so I assume the wood and plastic are more energy efficient but require more finesse to form. Current technology can't synthesize real wood, but what it can do is turn produce oil from carbon and hydrogen, and of course we know how to turn oil into plastic. Is that entire process more energy efficient than the whole processing of finding, digging, and refining iron? I do not know. It could go either way. But if you have a limitless fusion reaction with you, the abundance of raw material could become more important than the amount of energy it takes to process it.
This starts steering things back to nanotech and molecular engineering again which I don't like to do. But it might be unavoidable because there is great incentive to travel light, but the paradigm of our industrial production is to do things big, but doing big things requires big equipment with big resources.
Hard-science wise there's not much room to budge because we are so far from it as we know it. You would either have to ignore the issue, hand-wave it away as something that's taken for granted, or come up with ClarkTech like Star Trek replicators.