Whenever possible, wear something appropriate for the character. I say whenever possible because sometimes you won’t be able to wear what the character would wear. You might be auditioning for the part of an alien. It might be for Henry VIII. You should never look like you’ve been to a costume fitting before the audition. This tends to make the actor look desperate. Just try to be correct enough. I say ‘correct enough” because even if your character was in a tuxedo and you own one I wouldn’t recommend wearing it.
A good rule of thumb is; what would you feel comfortable wearing to your neighborhood grocery store? You might dress up in a suit and tie, but a tuxedo or an evening gown might be too much. You might wear jeans and a plaid shirt but maybe not with chaps, spurs and a ten gallon hat. You never want to seem like you’re trying too hard. You want to show up in an outfit that respects the idea of your character but never makes you seem like a keener. Extra credit, apple polishing, goody goodies rarely become movie stars. Avoid showing up to the audition in “costume.” Always remember to hang on to a little of your dignity. It can come in handy.