What architecture styles and any similarities to the clothing forms or embellishments and motifs existed during the Ancient Greece--Archaic to Classical--time period?
Speaking only of the Classical period, which ran from 750-336 B.C. approximately, this was the most intellectual in terms of arts, architecture, politics, and philosophy. This was the epoch which followed the fall of the Mycean civilization, which itself led to the Greek Dark ages (1100- 750 B.C)
Coming into the light after a time of chaos was like cleansing an old slate and starting anew for the Greeks. This was a period of simplicity, elegance, focus on softness and sophistication. Undoubtedly, as it happened with the Myceans and even the Minoans, the social structure was also evident in the clothing.
In this period the formula for building came in the form of the Doric and the Ionic style. The Doric order is evident in the Parthenon where the top of the columns denote the what looks like a base while the base is bare. It is like an upside down column.
If you notice, the clothing of the Classical Greeks (cloak, chiton, himation) tends to imitate the architecture of the time in the way that it flows all the way to angles without much decoration and the bottom; the focus (albeit not exaggerated) continues to be on the top of the garment. Also, the Doric columns have ridges, also known as fluting. If you look at the classical tunics, the way that they flow down folds as if it were fluting as well. These are called the Doric peplos.
The Ionic period came with the Ionic chiton.This chiton was mainly worn by women; it was fuller and longer than the Doric peplos. The Ionic architecture features a more complicated top which curves and curls in itself like the horns of a ram. Interestingly, the Ionic fashion was somewhat more complex as well; the chintons and himations had more fabric and felt thicker. There was also an early exploration of adornments and different accessories, and in the use of the himation.
The picture below shows the differences between the Ionic and Doric period dress, which indeed shows a tendency to repeat the patterns of architecture, creating a uniformity that greatly permeated the psyche of that society. It is impossible to not feel the vibrant atmosphere even in a replica of daily life in classical Greece.