When I first got into card magic, I wanted to learn a false cut and that led me down the path of one-handed cuts. They were flashy, they were fancy, they were awesome. They weren't, however, false. But, that was okay because they were the foundation of what would later become a collection of one-handed false cuts I still use to this day.
This tutorial contains the first three one-handed cuts I learned and I recommend any beginner to start with too. The Charlier Cut is the most basic, but also the best foundational one-handed cut. The Scissor Cut is a little flashier and will need more hand dexterity, but do it right and it'll hold it's own place in your repertoire. The Revolution Cut is the hardest of the three and while less useful in magic, it'll be a near-requirement for any more advanced cardistry cuts whether they need one or two hands.