I try to fly a ship that not too many other players are flying. Easier said than done, of course.
I don't like the ASP Explorer because it's design is just like a Cobra. I don't like the bloated, stubby ships like the Beluga and Keelback. And I don't like tiny ships.
So I fly a modded DBX. I really hate that name, though - 'Diamondback Explorer'. The name evokes the image of a fat man with a crusty, hairy back. If it wasn't for the DBX stand-out aesthetic, it's name - and that aforementioned image it evokes - would be more than enough for me to have never bought it.
I wish Frontier were better at naming ships.