I didn't realize there were people who don't rinse after brushing. I rinse with water 3x: after brushing, after flossing, and after rinsing with mouthwash.
You're not supposed to rinse or drink any water after using mouthwash for 30 minutes. It reduces the effectiveness.
If it has fluoride, absolutely, but mouthwash that doesn't contain fluoride, i.e. Listerine, doesn't have any such restriction.
With fluoride in city water and my toothpaste, I don't bother with flouride mouthwash, but those who have their own well, probably not a bad idea.