The Roman Republic, and later, the Roman Empire, was heavily influenced by Greek culture, in everything from its literature to architecture and fashions. Much of our knowledge of early clothing comes to us from works of art, salvaged in part from archeological digs, and now residing in museums all over the world.
The standard Roman garment was the tunic, commonly called the T-tunic as its cut was basically the shape of a T. Over the tunic, men wore their togas, if they went to the Forum. Commoners usually wore plain brown tunics of wool. Yes, even in the summer, but their wool was not what ours is today. Rather it was a soft weave and could be worn in the summer. Patricians or nobles wore garments of linen and silk, usually ornamented with a band (or bands) to denote their office or status.
Women wore tunics, too, and since most of what we know comes from extant art, which more commonly depicts well-off citizens, the elegant draping of garments during this period looks much like Greek fashion; over a lady's tunic, which might only come to her knees, she wore a stola, a floor-length dress styled much like our 'jumpers', and clasped at the shoulders with ornamental fasteners. Over this came a palla, a shawl of sorts, worn draped around the shoulders or waist. In cold weather, she wore a cloak, sometimes hooded.
An interesting website, with terms and careful description of articles of clothing, can be seen at www.uky.edu/AS/classics/jlsgloss.html.
Clothing changed little until the 5th century, an era we call Byzantine, a term coined later and one the Byzantines themselves never used. Byzantine dress is fascinating, and I'll blog about that later.