Final Fantasy X is probably the best Final Fantasy to start out on, whenever I introduce a friend to the series I always start with X. It's a well rounded game in all areas, it's beautiful, has voices, is easy to pick up and understand, and very user friendly. I got my ex-girlfriend into the series and I did it in this order:

Final Fantasy X > Final Fantasy VII > Final Fantasy IX > Final Fantasy VIII

Next I will suggest that she plays Final Fantasy VI.