Waistbands. There is no need for debate.
They do go in the middle of the whirlygig, not because I care whether anyone sees my knickers or not, but because the outer lines are a bit higher up, so the sheets and trousers and dresses have to go on the outer lines. Also, knickers and socks aren't likely to wrap themselves round the central pole as bigger clothing might, if it's a bit windy.
And if anyone's going to say that it doesn't matter which order you hang your washing up in is just Wrong. It is also Wrong to have mismatched pegs on a single item of clothing. (This is easily resolved by buying only one colour of pegs. Except I can't throw out the existing ones until they fall apart.)