If the school has a school uniform policy, it’s likely that they would hold rigid standards about the way a student should dress. By finding out whether the school is super strict or just conservative, you’ll be able to prepare your apparel accordingly.
If the private school is fairly strict, go for something like a pair of slacks or a skirt. For boys, wear a collared shirt or at least a t-shirt with no signs, symbols or pictures on the front. For girls, go for a shirt and slacks or a modest skirt with a pair of flats. If the private school is not so strict, you can probably get away with a more casual look and even some dark jeans (with no rips or holes). Wear something nice and avoid features that make huge statements. Clothing can tell a lot from a person, so try for limited make-up girls and no hats for boys.
On the drive to the school, possible think up at least one question that you can ask the interviewer when prompted; this shows that you have an interest in your education and will be a valuable asset to the school.