If I recall correctly in order to start using a brand new class you have to go to the guild first. The first quest you do will give you a weapon. So in order to start Arcanist you will have to travel to Limsa. There used to be shops in all cities that sold level 1 weapons but since the guild unlocking requirement has been added to ARR the only place to get starter weapons is the guilds. If you want to start in a city that doesn't hold the class you want because of the starting story. You will just have to get to level 10 in a class of that city then travel