Our Sun will eventually:

A explode in a supernova.

B become a white dwarf star.

C become a black hole.

B. become a white dwarf star

It will swell, shed its layers, and become a white dwarf star.

I know the sun does not have enough mass to become a supernova or a black hole.

B. Become a white dwarf star.

Explanation:

As the Sun is a medium size star in mid of its life of around 10 Billion years. When it will exhaust all the Hydrogen in the core, it will go through a long process of death: Converting into a red giant to Planetary Nebula to a white dwarf. It will spend trilliion of years in white dwarf phase before fading and converting to a Black dwarf.

If it had been a massive star it would have made a Supernova and then ultimately a black hole or a neutron star.