What sort of clothes do I need to work out?

I’m a swimmer and that’s generally only exercise I ever get. I’ve never really lifted weights, but I want to start.

I’ve never had to deal with gym clothes, really. I have some gym shorts, but my only underpants are boxer shorts.

This might be a stupid question, but do I need to get tighty whities for the gym? You know, because boxer shorts are open on the bottom…