Sport bike is sometimes used to describe a road bike with light-touring capability, they make excellent general purpose bikes but are a rare breed.
Most city commuters can do without suspension, its adds weight and maintenance.
You need to decide what size tyres are most appropriate for your riding. For MTBs it is probably a 1.5-1.75" slick, for hybrid bikes a 28-35mm and for a road bike a 25-28mm. You need a frame with suitable tyre clearance; road bikes can sometimes struggle to fit medium tyres such as 28mm.
You probably need threaded eyelets for a rear luggage rack and fenders. These are always useful on a commuter even if you chose to use a backpack. Even a road bike with eyelets can haul a heavy load of shopping a couple of miles. Clip on solutions such as seatpost racks carry less, weight more and are not as stable. Same goes for fenders: bolt-on fenders always perform better than clip-on versions.