I hope I can answer your question. It has not been very well worded so I may have misunderstood, for which I apologise.
To my mind, the most important characteristics of an example are:
- It unambiguously illustrates the point you are making.
- It is related to the topic in hand.
- Wherever possible, it does not contain too much additional information.
These are not "rules" but common sense criteria. Additional criteria for selecting examples will largely depend on the topic and nature of the essay.
An engineering or pure-scientific paper could make use of hypothetical cases, either well-known in the field or constructed specially by the author, to demonstrate the principle being discussed. Such examples should be complete and coherent; as simple as possible without being trivial; requiring as little supporting material as possible to demonstrate the core principle, thus preventing distraction.
A practice-based topic (such as medicine, law, social work or business studies) should usually use real and referenced cases to illustrate a point. This usually requires much more extra information than would be acceptable for examples in other fields, but this can often be resigned to appendices.
Humanities, social sciences, languages, arts and other less prescriptive topics usually require a broad coverage of examples in order to substantiate an argument. For this reason, examples should be as brief as possible (within reason) and from as wide a variety of sources as possible. If your examples must come from a single source (as with literary analysis) then examples should be selected from the full body of the work rather than a single verse, chapter, character or whatever. Of course, if you are able to provide material from outside the work in question to support your point, this is usually very well received.
Note that the above point about multiple examples is true when making an argument, but when making a counter-argument (ie disproving a previously proposed argument) it is generally only necessary to provide a single and conclusive counter-example, unless the counter-argument is the main theme of your work.
Bear in mind that it is often considered poor practice in academic works to use archetypal examples to illustrate a point. If you make reference to examples that are already very well known to practitioners in the field, your paper will come across as lacking any depth of research and therefore lacking authority. Sometimes this can be subverted, perhaps by presenting a new or unique insight on a well-established precedent, but only if you're certain you know what you're doing.
The best possible advice is to read other papers in the field to find out what works and what doesn't - which you will be doing anyway as part of your research, of course!