What do we think of as necessary?

A friend of mine asked me recently: "What occupations are necessary for society?"

In order to answer this, I feel it's important to make an important distinction. Is there a difference between occupations necessary and services necessary? I distinguish because for example, I posit that people need some enforcement of law and order. However, I argue that such a service can be self-provided and not necessarily an occupation.
The same friend asked: "what if the society in question is peaceful?" In this and the rest of the following situations, I'm not focusing on a specific facet, but rather the fundamental nature of each idea. So take "enforcement of law and order" to mean arbitration of differences. Along those same lines then, medical care of some sort or another is also necessary. Trade, additionally, is also necessary. Not simply "merchants". Trade is what sponsored the development of ALL major societies that currently exists. When "America" wants to threaten a nation nowadays, it cuts off their trade with embargoes and the like.
So it can be said that each of those are necessary as "occupations." However, extensions of those are also necessary. In order for merchants to exist, trades that produce goods or services must exist as well. Where one draws the limit on those extensions is the real question. As an example, farmers are an obvious choice, but where, in another instance, do the yoga instructors fit in as a necessary traded service?
Now we get down to the tricky part of this question. What it seems you're looking for is a core essential group. What you realize is that in order for an infrastructure to exist, there needs to be an exostructure for it to support. In other words, you can't really have a heart without a body for it to grow in. The two sides are symbiotic. It falls to opinion whether any peripheral services are therefore necessary or just luxury(if indeed luxury isn't in some form necessary!). Minutia on this point can be argued to almost ANY degree depending on how you want to see it. Even said yoga instructor can be argued to be vitally important if you look at it from a point of view that says that facilities which maintain wellness are essential.
The counterpoint to the question "what occupations are essential" can be stated easily as "what occupations are NOT essential" and be just as valid. Society as a living thing very much dictates it's own needs and functions. Taking a look at occupations that no longer exist is an easy way to answer the question because clearly society has chosen them to be slotted for obsolescence. Anything that currently exists suggests that it IS actually needed. Or at the very least until our society changes and with it, our needs. The only way to get any sort of answer to this question is to establish parameters for a society at a given point in time. Even then, the only sort of answer you'd get is one which, by it's nature, is no longer relevant to the modern day.