I actually really enjoy thinking about what my character is wearing. It helps me visualize the adventure and setting.
My longest running 5e character was a dwarven wizard archaeologist who had been banished from his hold, named Drustan Green. I started with him having a well-worn green cloak that kept him protected from the elements as he traveled about the wilderness, seeking out ruins. Over time as he became more powerful and opened up a series of museums, his clothing improved, and he got one of those breastplates with the muscles carved into it. He would also purchase clothing in different towns, especially those with different cultures. His winter weather gear was made by Goliaths from the hide of a giant rabbit, complete with bunny ears on the hood.
In the games I run, I like to give characters opportunity to purchase unique clothing. I once had a shop in a wealthy town that sold really, really fancy hats. They weren't magic or anything, they were just really, really fancy. The characters couldn't afford them, so they demanded the fancy hats as a reward for completing a quest. It was memorable and now everyone had a fancy hat!