What type of wire to use in underwater applications
Use submersible pump cable -- it's what's listed and tested for the job

Submersible pump cable uses a different jacket and insulation composition than other wet-location cables, as it must meet standards for potable water use (NSF/ANSI 61, to be precise) as well as the applicable electrical standards.  The downside is that it must be run in conduit if it exits the wellbore, as it does not have quite the mechanical durability of a direct bury cable.