Take that out. It doesn't matter what sort of job you're applying for -- the words "high school" should never appear in the resume or cover letter of anyone who has a college degree.
As for the rest: Dress like the job you want to have, not like the job you're applying for. If I was applying for a management position at a bank (not that I can imagine why I'd ever do that, but hypothetically...) I'd still turn up for an interview wearing a t-shirt and jeans. If my apparel wasn't up to standard, that would be an indication that the job I was applying for wasn't actually a job I wanted -- and being not offered the job would simply save me the trouble of quitting after a few weeks.