Creative and artistic data visualizations communicate stories and invite engagement, yet how designers develop their expressive forms remains poorly understood. We investigate the design process of data artists through three complementary studies: an analysis of 40 public project accounts, artifact-anchored interviews with seven experienced data artists, and a design task-based study with eight data artists. We find that stories and visual forms develop together through data exploration, reference adaptation, sketching, and prototyping. Inspiration comes from data, existing work, everyday imagery, and personal experience. Sketches help develop mappings, while prototypes with real data can reshape representations and intended stories. Designers consider multiple possibilities but typically develop one direction at a time, partly because producing alternatives is costly. Their choices balance meaning, visual appeal, readability, and feasibility. These findings inform tools connecting stories, references, and real data, including AI assistance that supports testing and revising alternatives while preserving designers' creative judgment.

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