The ubiquity and on-the-go availability of mobile devices makes them central to many tasks such as interpersonal communication and media consumption. However, despite the potential of mobile devices for on-demand exploratory data visualization, existing mobile interactions are difficult, often using highly custom interactions, complex gestures, or multi-modal input. We synthesize limitations from the literature and outline four motivating principles for improved mobile interaction: leverage ubiquitous modalities, prioritize discoverability, enable rapid in-context data exploration, and promote graceful recovery. We then contribute thirteen interaction candidates and conduct a formative study with twelve participants who experienced our interactions in a testbed prototype. Based on these interviews, we discuss design considerations and tradeoffs from four main themes: precise and rapid inspection, focused navigation, single-touch and fixed orientation interaction, and judicious use of motion.