Consider the following tech tree.

• The rocket can double as a living habitat, if it manages to land in one piece. Martian dirt could be used to re-inforce the walls to protect against radiation.
• Solar energy with a battery or nuclear could serve as a power source.
• Water can be extracted from regolith (martian rock) by baking the regolith in a furnace, the water evaporates and can the be re-condensed.
• Oxygen can be produced through the electrolysis of water. One kilogram of water produces approximately 880 g of O₂, which is roughly enough for a day per person.
• Methane can be produced through the Sabatier process, which takes as input H₂ and CO₂, and can be used as a rocket fuel and to make bioplastics out of it.
• Plants are the tricky part. I will create a further post later in the future to give more detailed information about this. The basic gist is that you can create greenhouses if you have the basic ingredients (mostly water).