For one-on-one dueling, using a weapon you can wear as a sidearm, the rapier has the advantage; that’s what it’s optimized for. If small group combat is a possibility, other swords might be useful: an estoc if you might encounter armor, or a curved sword if you need to move quickly between multiple opponents.

I would rule out the epee and small sword. They are basically rapiers that sacrifice effectiveness in order to be less cumbersome as fashion accessories.