Does the universe prefer a velocity?
There is a preferred standard of rest, that of the Cosmic Microwave Background (CMB). You can detect motion with respect to the microwave background. So move fast with respect to the background and the CMB in the direction of motion will be blue-shifted and in the opposite direction will be red-shifted compared to a direction orthogonal to the direction of motion.

The Earth motion has been measured with respect to the CMB, see here

You could/can also detect your motion from the anisotopy of galactic red-shift in the same way.