No, mouthwash after brushing removes the fluoride that the toothpaste has just deposited. Similarly, avoid rinsing after brushing.
There's not really a 'good' time to use mouthwash. Maybe an hour or more after a meal, if you're in a rush - but no sooner than that, as the tooth enamel will still be softened by the food.
For whatever reason, (in the US) mouthwash contains far less fluoride than toothpaste.
So, mouthwash before toothpaste. Or do as I do, and use mouthwash intermittently when in the bathroom, to boost the time there is fresh fluoride inhibiting bacteria on my teeth and gums.
Most importantly, don't rinse after either - same idea.
There's not really a 'good' time to use mouthwash. Maybe an hour or more after a meal, if you're in a rush - but no sooner than that, as the tooth enamel will still be softened by the food.