Should I really wear "fancy" clothes to a job interview?

I've never had a job before and as a freshman college student I'm looking into this. A job I would like to start off would be Starbucks. I want a simple and not so complicated job and I've researched my area and they pay well for my position / role. But is this whole wearing a suit, tie, fancy clothes an actual thing I should look into especially for Starbucks (a present millennial like company)?

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