I don't have all the answers, having played quite a while ago and not having finished all the content.
Ambitions are definitely unique and take many steps to go through. Such steps are sprinkled throughout the game, across the span of skill levels you will acquire.
Basically, your first choice will give you access to a number of Storylets that start this particular storyline with beginner-level tasks. Once you're done with this, the next step will have a task requiring a much higher skill level, so you will have to go through a good deal of the other content before you come back to it. At some point, the "next step" will require access to restricted locations which, again, requires a certain skill level or acquiring unique items.
You can cancel your Ambition by going to the NEX tab and buying the Nethean Tea Leaves. This costs 50 Nex, which means it will quite certainly cost you real-life money. I have no idea if doing this once done with a first Ambition (most likely at the "end" of the game) allows you to start anew with a different one. It's possible, but be aware that your skills would be such that you would most likely breeze through it, which may dampen enjoyment.