One reason communities build storage dams is to ensure there is water during dry periods.
Its the same in households, storage tanks big enough to carry over the dry spells enable people to live in them.
It is necessary in budgets to allow foir tanks, thinking they are costly
should not be an issue, since
land purchase, shack building etc would be more than a tank.
You need to work out the volume of water you will need for say 3 months, rainfall data will tell you how many dry months there are.
The tank should be that big at least.
Extra catchment can be created with tarps hung around and draining to the tank.
As for lifting water from the creek when it rains, its possible.
Some questions?
Can a tank be installed above the elevation of the shack so gravity works for you?
Can a pipe be fitted into the stream diverting water to the tank without using a pump?
If
the answer to these questions is yes, then building a small dam with a leaf and stick trap would work well.
Depending on the distance from the dam to the tank, the biggest size pipe the budget will stand is best.Sat 90mm stormwater would be great down to 50mm poly pipe.
The tank will fill faster with he bigger pipe.
A smaller pipe can be connected to the shed, say 1 inch and it will be adequate for flow and pressure. Assuming you have at least 4-5 meter height distance between the bottom of the tank, and the top of the shack.