It's partly down to basic physics. A well engineered pump can suck water up about 15ft but not more. Even then any leakage in the pump will make getting water to the surface hard work. Once the pump has water in it, it is more efficient. It helps to prime the pump with a bucket of water as you start pumping.
I know this from my Grandad's small holding where he relied on a shallow well with a half rotary pump meant for pumping oil and fuel (ex-WW2) . Corrosion meant these pumps only lasted about 5 years.
If you could put the pump down the well below water level it would work much better and any depth would be possible. Look at the 'nodding donkey' pumps used in established oil fields. The rod going down the well to the pump is balanced by a weight on the opposite side of the frame at ground level. The small engine driving a crank to operate the pump then only has to lift the oil (or water). For your needs, the motive power could be a lever with a weight on it.
However, it would be much easier to buy a submersible electric pump for about £50 if you have a supply of electricity available. If not, a portable generator and a water tank would make a workable proposition provided you don't mind hauling the generator out of a secure store when water is needed.