Personally, I'd love if the series took place during the missing time period between Episodes III and IV, and maybe focus on the backstory of a young Han Solo and Chewbacca back when they met, how they came to be partners, etc. And you can of course introduce a whole range of new characters or even younger/older of characters from the old/new trilogies.
As far as a show about all new "minor" characters, I will quote from the movies and say "I have a baaaad feeling about this...".