Can you contact the instructor for the section of class you want to take and ask what they require?
When I took the BRC (in SF), we were required to wear a long sleeve shirt, jeans, glasses/sunglasses/or goggles (only if the helmet did not have a visor), over the ankle footwear (I wore my hiking boots), and gloves (preferably leather). They had helmets there for people who needed them. I wound up borrowing a helmet, jacket, and gloves from a friend for class.
Most motorcycle dealerships sell gear…go and try on stuff and sit on a few bikes
I found the salespeople really helpful for getting the right fit on the helmet. I would have probably got the wrong size without their help. I wound up finding the jacket I liked cheaper online then at the store. In total I spent about $750 on gear (i splurged on my helmet)… $600 sounds like a very reasonable budget for gear.
Best of luck on your class!