The basic needs of the colony can be put into a few categories:

Some planets are more habitable, some less. You could get lucky, and arrive at a planet with a significant atmosphere and even liquid water. You could also be colonizing a planet with no liquid water and no atmosphere - that’s going to make your life a lot harder. And don’t even attempt to colonize a Venus-like planet until you really know what you’re doing.

The most important materials for life are oxygen, carbon, hydrogen and nitrogen - the rest are present in such small quantities you can survive on stocks for a very long time, especially if you don’t let your population expand too fast. Recycling is the key on hostile worlds - the only input you need is waste and some energy to process it. Most of the colony is a closed environment, which lets very little waste go unchecked. We have brought a range of plants and bacteria to help break down personal waste and establish the basic air/food cycle. While those processes are extremely energy inefficient (just a few percent of the input energy is actually stored in the food - the rest is waste heat), they are very simple to implement and need very little maintenance, making them cheap in the early days of the colony. Eventually, we’ll want to supplement these with more industrial processes, where we have much better control over the output - and better efficiency and rate of production.

Radiators

Water

Oxygen

Carbon

Hydrogen

Nitrogen

Calcium, phosphorous, potassium, sodium, …