Common law is the same thing as case law.
The idea behind "Common law" is that you develop a set of rules through cases. Common law and the use of precedent are just a complicated way of putting into practice the idea that later cases must follow earlier cases unless there is a very good reason not to. Over time, applying that basic idea results in old cases actually constituting the law, because if you want to know what the law is you must look at old cases. In common law areas cases ARE the law.
When looking to establish where a particular rule comes from, then you cite cases because those cares ARE the law.
Because of the way it is, common law can change all the time. The law laid down by old cases might gradually change over time as new cases apply it in different ways.
When choosing a case to cite, you often have multiple options. Broadly, you can cite 1) the case where the rule first came from, 2) a case which explains the rule (it often happens that an early case applies a rule but a later case explains that rule in a lot more detail) or 3) a case that applies the rule to a particular situation. Usually you want to go for 1) and usually you want to go for a House of Lords rather than Court of Appeal rather than High Court case, but its context dependent.
Rules like offer and acceptance, consideration and intent are so elementary and have existed for so many years that I don't think you need to worry so much. The law is what it is because that is how courts make decisions: there is no definitive written "law" in the way that there is with an Act of Parliament or a Civil Code as in European countries, in many ways the study of law is the study of what decisions courts make and why rather than a search for anything more abstract. They are applied by hundreds and hundreds of contract cases so there is no doubt that they are the rules that are applied. One would usually cite a House of Lords case that directly applies or explains the rule - for offer and acceptance, Smith v Hughes is often cited, and for consideration, Re Pinnel's Case is a good choice since that case explained what consideration is.