Max said, Technically it's not a well but a spring that's been channeled in a sort of reservoir but I'll just call it a well because functionally it's the same I think for this purpose.
For what you are describing, we use a submersible pump.
To me these are very versatile pumps and can be used in lots of situations.
By the way what you are describing, on Homestead Rescue they call that a well, too.