A Vision
Appearance
Rei's distinctive blue hair and red eyes may at first seem like it was picked for aesthetics, but it's most likely more significant. As Rei is a clone, her strange colorations are suppose to suggest that. Clones are supposely more inclined to be albino, and Rei's red eyes are one clear suggestion that she is albino. Her pale skin also fits the bill.
You can usually get an idea of who a person is by what they dress. Rei is only ever seen in the series wearing her school uniform and her plug suit (what they wear when they pilot the Evas). She wore a swimsuit when the occation called for it, but there is no casual clothing she is ever seen in, canonly. It's only in artbook pages and extra media that Rei is ever seen wearing everyday clothing or anything other than her school and pilot uniforms. I think this signifies that Rei's life revolves around her duty. She goes to school only because she has to, and spends most of her time at NERV headquarters. That is her life. Her mirror opposite is Asuka, who happily lives her live full of non-school and non-Eva related hobbies.
While Rei seems to live her life as if trying not to stick out, being noticed only because of her quiet nature, one thing in particular I always thought did stick out: her socks. While the other students wear average white socks, Rei wears an unique black pair of socks. There is never a reason given, or any hint at why that is. I really can't think of a significance, but her black socks always made me feel Rei was different and special. Perhaps the difference in sock color was just Gainax's way to visually identify her to us as being different.
Rei's stoic and expressionless face is also kind of a trademark of hers. Before Rei, this kind of female character was not that popular, if it even existed. After Rei though, her appeal was pretty big and this kind of female character became one of those "moe" factors. I always think of her as an early pioneer of that look. Later anime series would follow with the quiet and strange girl persona.