cherrybim,
The Elya Rabba says that the Rabanan in the time of the Gemara wore white garments on Shabbos.
The Kitzur Shlah (Siman 135) and The Mateh Moshe (Siman 414) say to wear white on Shabbos.
The Aruch Hashulchan (Siman 260:1) says that today, wearing a white shirt on Shabbos suffices.
The MaHaram Chagiz (Siman 543) says that wearing white on Shabbos is a Tikkun (rectification) for Aveiros related to Arayos.