1. Heraclidean. Geo-heliocentric. Mercury and Venus circle the Sun; everything else circles the Earth.
2. Ptolemaic. Geocentric, stationary Earth.
3. Copernican. Heliocentric, pure circles with lots of epicycles.
4. Gilbertian. Geocentric, rotating Earth. (proposed by William Gilbert in De magnete)
5. Tychonic. Geo-heliocentric. Sun and Moon circle the Earth; everything else circles the Sun.
6. Ursine. Tychonic, with rotating Earth.
7. Keplerian. Heliocentric, with elliptical orbits.
See:
* https://tofspot.blogspot.com/2013/08/the-great-ptolemaic-sma...
* ToC: https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-sma...
* PDF: https://faculty.fiu.edu/~blissl/Flynngs.pdf
By the mid-/late-1600s people leaned toward Kepler, mostly because the math was easiest.
With regards to evidence for the Earth's motion, the first inkling was in 1728 with stellar aberration with in γ-Draconis:
* https://en.wikipedia.org/wiki/Aberration_(astronomy)#Discove...
The first for the rotation of the Earth (around an axis) was in 1791 by Guglielmini:
* https://en.wikipedia.org/wiki/Giovanni_Battista_Guglielmini
We finally got parallax in 1806 by Giuseppi Calandrelli in α-Lyrae.
Stellar parallax was considered since at least Aristotle, as he mentions in his On the Heavens (II.14), and since it is not observed then it is reasonable to conclude that there is no motion (it took several thousand years to develop instruments to actually measure it).
Daniel Whitten's "Matters of Faith and Morals Ex Suppositione" is an interesting read.