My father was famous in the 50's as a soap opera actor. My Mother also was in the professional theater. Fame has several taxes. Loss of a normal life. There is "Intrusive public", who like you only because of your face. Therefore, you are really constantly irritated once you get your fame. You either serve all of the adoring worshipping people with signature seekers, or you are called names for not serving the adoring people who don't really like you anyway.
I have heard many many many jokes over the years from my father, his friends, and also just interviews that FAME is great for getting seats without reservations at great restaurants.
Sometimes, as fame goes on, it limits ways you can make money. Mickey O Rourke wanted a construction job. No one would hire him. Fame also gets you unemployed when you are too far up. Fame for musical artists is that they are constantly judged against their highest days of achievement. Anything less than that and you are called a "has been".
Money, if you can conserve it, is usually yours if you hit a certain level of fame. In answer to the question, I would like to be famous as a writer, and then no one would know my face! Ahah.