What type of pumps will provide 4 gpm at a 1,500 ft lift?

A low flow high head centrifugal type pump can work or a PD pump.

 used Reciprocating   plunger or diaphragm pump 

Just piston pump , centrifugal - no

Vertical turbine and double suction pumps,  one-line jet pump can typically,  50 HP submersible pump