The burgundy suit is not seen very often these days. This suit is certainly inappropriate for your everday office or business setting and is not favored in most formal settings either.
Today you will find that the only places you may see a burgundy colored suit in church, special men's organizations, and the odd semi formal party involving the use of a suit.
Pale complexions rarely pull this look off well as this shade does not favor the color white. Keeping this in mind men with the right skin shade should make sure not to pair this suit with a white shirt.
Shirt colors that go well are darker contrasting colors such as the use of a black shirt in combination with a nice pair of black shoes.
Another look would be a flamboyant yellow shirt like the one Peter Gabriel wears in his video for the song steam.