According to the script of the episode, the pronunciation for Barradis was "buh-RAD-us". 
According to the Star Trek: Star Charts, on page 45, the Barradis system primary was a Class K star. It had a magnitude of +5, which was the same brightness as Sol. In the distant past, about 2,000 years ago, this system was a stop on the Debrune trade route. This system was located in the Beta Quadrant.