Cutie and the Beast is a contemporary romance manga. It's licensed by Seven Seas. I bought my copy brand new.
Review:
At the end of the first volume, Momoka's parents caught her and Kuga in a loving moment, after Kuga asked Momoka to marry him one day. Momoka's father is understandably displeased with what he views as an adult pro wrestler toying with his starstruck teenage daughter. Kuga becomes determined to win him over and show how serious he is about Momoka.
And that's the bulk of this volume. We get a flashback to Kuga's past, early in his career as a pro wrestler, and Kuga and Momoka go on a date (or at least attempt to), but the largest portion of the volume was devoted to Momoka's dad sternly staring at Kuga and Kuga bringing gifts and doing anything else he could think of to win him over.

