Do flight schools typically have dress codes or expectations?
If you are learning to fly as a hobby and are paying the school your painfully earned money, you can dress however the hell you want, within reason.  Formal attire in that circumstance is ridiculous.  If you are in a professional school in some airline related program, or a government subsidized school with a formal dress code, that's another story, and you follow the rules as they are.  

Anyway, the problem with hoodies and track pants is really loose clothing and hoods can be a problem in a cramped cockpit and especially if trying to get out in a hurry on the ground.

A cotton or wool shirt without a hood and good pockets, and cotton or wool cargo pants (cargo pant pockets are really handy) is my favourite dress for flying.  Avoid "plastic" synthetic fabrics.  Having fibres made from plastic, your clothes will melt into your skin if things get "hot".  

Same with shoes.  Wear shoes that will let you walk at least some distance on a rough surface.  You may find yourself walking a mile over rough terrain after a forced landing.

Dress for comfort and contingencies, without getting carried away (like buying a nomex flight suit) in other words.