Why not wear a toga? The toga was the formal and official civilian dress of the Roman citizen. For your recitation, you will want to dress like an ancient Greek, not a Roman. Men and women in ancient Greece (and Rome) generally dressed alike, and the clothes were usually handmade. Below are some examples of the most common garments worn in ancient Greece. You should find a costume appropriate to your character. For more descriptions and illustrations, browse the vase painting in Perseus by keyword: Also check out the "History of Greek Costume" site.
Greek God: Dionysos wears a long chiton (tunic) and himation (cloak). Apollo is garbed in chiton embroidered with crosses, boots with curled flaps, and himation with striped border hung over his arms. His long hair is bound up in a heavy bunch at the nape of his neck by a fillet wound twice about his head and tied at the back.
Greek Goddess: Hera wears a long, transparent Ionic style chiton with elbow sleeves and a dot pattern at the bottom; a himation is draped over her right arm and shoulder, leaving her left arm exposed. Demeter wears a peplos (Doric tunic or dress) with a black border, a radiate crown (stephane), and a veil which covers the back of her head.
Greek Hero: Oedipus wears a short chiton and a mantle; his petasus (hat) hangs at his back from a red cord. Herakles wears a lion skin over short chiton and a scabbard, while Andromake, queen of the Amazons, wears a short-sleeved chiton with a belt, the chiton is decorated with registers of animals and mythical creatures: a sphinx, three sirens and four felines facing alternately left and right. She is armed with an Attic helmet, a shield and a spear, and has a sword at her side. Penelope (or Helen) might wear an elaborate chiton, with a himation drawn up over her head (woman on L); a younger girl might wear a full pleated chiton and a wreath in her long hair (girl on R). A Trojan king Priam here wears a chiton of thick wool, bordered, and fringed at the ankles; over it, a himation. He carries a sceptor. The Greek warrior Neoptolemos wears a corslet with metal enhancements, and a helmet of Attic type. The caul of the helmet has a lozenge pattern, the cheek-piece is black, the nasal plain, the frontlet moulded into the likeness of curls, the nape-piece ornamented (as in the other Attic helmets on this vase) with a black pellet. The lozenge-pattern indicates a cloth covering, glued to the metal, against the heat of the sun.
Maenads wear ivy wreathes in their hair and carry a thyrsus. They are dressed in long chitons, and himatia of 'Ionic' mode. The other maenads wear the chiton only; in the woman at the altar the girdle is concealed by the kolpos (gathering of fabric that falls over the belt); in the other it is exposed. The women have bracelets.