Shoes
Shoes matter more than anything else. You want something that grips enough to be safe but slides enough to turn. Good choices are dance trainers or shoes with a suede or smooth leather sole, or cowboy boots with a leather sole. Heavily treaded trainers grip the floor while you turn, which strains knees.
Clothes
Wear whatever you can move in. Classes get warm — layers help. Some socials have a theme or a western dress code; it'll say on the event page.
Boots and hats
Lots of people love the western look and plenty don't bother. Modern line dancing is danced to pop, Latin, Irish, rock and country, so jeans and a T-shirt are perfectly normal.