Not sure which class/job to choose

[Niwashi]

I assume that picking one and leveling it first to experience the story is a good idea.

Particularly if you're going to a preferred server, I'd actually recommend picking at least a couple to alternate between as you go through the story, and maybe more if you want to do any of the sidequests or other optional content as well. If you just have one, you're going to drastically out level your story progress. It kind of trivializes the story quests if you're playing them on a job that's way above your quests' level.