Given the artist's preference for smooth, flowing paint with vibrant color and considering that she has many months to finish the commission, the best choice for her material would be Oil paint.
Oil paint tends to have a rich, vibrant color palette and allows for smooth blending and layering, which aligns with the artist's desire for a flowing quality. Additionally, oil paint has a long drying time, giving her the flexibility to work on the painting over several months without being rushed.