> What are the most promising hypotheses for why galaxies rotate?

It's simply conservation of angular momentum. To steal from this article:

> Structures rotate because of a property known as angular momentum. Angular momentum is a measure of mass and rotation, and it is a conserved physical property. One of its characteristics is that when mass moves closer together, it spins faster to keep angular momentum constant. You see this in figure skaters when they leap into the air and pull their limbs close to their bodies. Galaxies, stars, and planets all formed from great clouds of cosmic gas and dust. As gravity caused these clouds to collapse, even the smallest bit of rotation was amplified. So it is natural that they all spin.

.

> What is the relevance of black holes?

Not relevant to galactic rotation.