I would install a submersible pump (purchased from a well supplier or from Lowes). However to use a submersible pump the well diameter must be 4" or larger. If the well diameter is 2" or 3" you must install a Jet Pump with a deep well injector.
NOTE: You can install a special 3" submersible pump in a 3" well, however I don't usually recommend it!
If the well is a 1-1/4" diameter and it's more than 25' to the top of the water I don't recommend any pump. A 1-1/4" well can be pumped below 25' using compressed air but that requires a more complicated system. If this is a must I can assist you with that as well!