LXHS is set in the year 1864 at a dress ball at Hogwarts. From reading the Harry Potter books, we know that wizards don't always have the best fashion sense, so it's up to the player how much one leans towards "historical 1860s garb" vs. "generic academic garb."
Women's fashion: Overall the look you see here will be one you associate more with Scarlett O'Hara and the American Civil War than with the exaggerated hourglass of the later Victorian period. Think hoop skirts and crinolines more than bustles. Women often wore many different styles of dress, with the detailing and neckline depending on the event and time of day; the type of dress most appropriate to this would be an evening or reception dress.
Men's fashionLuckily, men's fashion hasn't changed much in hundreds of years! Specific resources are provided below, but dress pants, vest, suit jacket, and tie would be appropriate in any time period.
You've got your graduation gown lying around? Got a red and gold scarf? Great, you're set to be a Gryffindor.
Given, you're at a dress ball, not in class, so feel free to have a lot more fun with it than that, if you want to. I recommend the Yule Ball scene from the Goblet of Fire movie, in particular.
If you want to embellish your outfit with the House colors, they are:
Gryffindor: red and gold
Ravenclaw: blue and bronze
Slytherin: green and silver
Hufflepuff: yellow and black
Please provide your own wand, if you are a magic-using character. All other props will be provided for you.