You could do that with the lancer, but you would be missing out on the vast majority of your tool kit. Dragoon has many useful, and much more powerful, skills than what you get access to as Lancer(unless they changed it since I got everything to 60).

As for the Grand Company, I know you can change them later on(and bounce back and forth every 30-days I think it is), but not sure if the initial joining of a GC can be done in a different city state than where you started.