I am more familiar with classical history and philosophy than with the rest of the eras regarding stars so this is only part of the answer. In Aristotle's cosmology, for example, the cosmos was divided into two parts. The two parts were limited by the moon and its orbit. In the sublunar part of the cosmos, everything was considered to be constituted by the four elements: earth, water, air, and fire. Things could be a mix of those elements, but they were complex, mutable and imperfect. However, on the part above the moon, everything was celestial, perfect, unchangeable. Here, heavenly bodies (stars, planets) would be made of some exalted and perfect substance, and even though they didn't change per se, they could move, thus already existing the notion of a circular movement and therefore the notion that stars and planets were spheres.
Hi, you may be interested in a couple of earlier answers