sump pump recommendations for storm water/sewer connection

I got a notice from the City of Oakland that my storm drain is connected to the city sewer system, which needs to be remediated.  As with many driveways in the flats, my driveway slopes down towards the garage/finished basement space.  There's a big drain at the bottom of the driveway, probably 3 feet below street level, which is the main source of issues.  I welcome any thoughts or advice about addressing this.  I'm assuming I need a sump pump -- does that sound right?  What should I look for in a sump pump system?  What happens if the power goes out during a storm?  Have you had any good (or bad!) experiences with companies that do this kind of work?  Will I also need to do my sewer lateral at the same time?  I'm apprehensive about the whole situation because right now our drainage is excellent, like, no issues in the big storm last October excellent, and I am not eager to mess that up.