How do you supply an opamp with -12 volts?

Voidugu:
Should I go for a rail to rail opamp or a single supply one?

Those choices are not mutually exclusive.

With a single supply one that works from 5V that is 2.5V per rail as you have to make a signal ground with two 1K resistors in a potential divider. Put a cap 0.1uF across each.
Then it is best to go for a rail to rail one to give you some swing to play with.