Given that the couple is naked, a major concern is temperature — especially at night. And with the additional possibility of rain, hypothermia is a danger. So, a shelter and fire are very important. A machete will help in the construction of a shelter as well as for other uses, like making a spear, as well as preparing food. And a fire is needed for warmth, boiling water, and cooking. Let me point out that without a fire starter, people had to twirl sticks to create an amber — and sometimes this proved to be impossible.
It is said that without water a person can survive for a week, and with water but no food, for a month. Perhaps for this reason the producers of the show made the duration of coping with nature 21 days.
So, in the order of priorities: shelter, fire, water, food.
So, why is this show so fascinating? Because this show makes explicit the human needs for survival. And survival is the bare bones of human life. Everything else is luxuries and psychological quirks.
Other than making such mistakes as drinking unboiled water and eating the wrong food (e.g. green figs), or not knowing how to hunt and fish, the main obstacle for successful cooperation is an individual’s character traits. Some individuals cannot endure the physical discomforts or psychological distress; others cannot cooperate because of laziness or ignorance, or because of being too bossy or too needy — and some are downright mean.
What this show teaches is that humans can survive even in the harshest environments as long as they have access to these environments. However, modern States which favor capitalism, forbid such a free access to subsistence land.
Below is an example of the show: