Consider the following tech tree.
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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.
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Solar energy with a battery or nuclear could serve as a power source.
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Water can be extracted from regolith (martian rock) by baking the regolith in a furnace, the water evaporates and can the be re-condensed.
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Oxygen can be produced through the electrolysis of water. One kilogram of water produces approximately 880 g of O~2~, which is roughly enough for a day per person.
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Methane can be produced through the Sabatier process, which takes as input H~2~ and CO~2~, and can be used as a rocket fuel and to make bioplastics out of it.
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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).
food production on mars is tricky. i'm actively investigating into it already. it's just such a complicated field that it takes me a while to actually make up reasonable claims.
what i've found so far is the following: if martian settlers get good support from earth, martial settlers could be fed daily, although it would be expensive. transporting a kg of mass to mars today could cost approximately $30K (with the technology we have today), and settlers need at least 1/2 kg of food per day. That makes for costs of about $5M per person per year (earth year), and that's just food. so a better approach would be desired. i'm actively investigating food production and i will definitely make a series of posts about this topic in the future, please be patient. thank you :P