Looking at old paintings of Romans ("Pompey in the temple of Solomon") they appear very different from what we now portray them as. Medieval and Renaissance drawings of them don't show any togas, lorica segmentata/hamata, etc. How would Julius Caesar & Co have been portrayed in Shakespeare's play at the time it was written?
I'm not a regular but I can answer. Actors were largely responsible for picking their own costumes. Generally, actors picked contemporary dress and costumes when going on stage. While acting greek or roman theater, actors sometimes wore togas for an "ancient" feel. Historical Accuracy didn't matter.
http://www.shakespearesglobe.com/uploads/files/2014/01/costumes_cosmetics.pdf