The Restatement is not law, but I guess you could say common law is grouped with it in the sense that the Restatement is reflective of what the common law rules are in some jurisdictions and perhaps what the ALI thinks the law ought to be.
The common law is the actual law (as well as statutes, regulations, and constitutions, of course.) It can and will diverge from the Restatement depending on the jurisdiction.
So when thinking about applying common law rules, think of it in two ways: (1) Jurisdictions that have adopted the Restatement approach into the law, and (2) Jurisdictions that have not adopted the Restatement into the law. The rules will be different in these cases.
Also, while the UCC applies to goods, it is not wholly comprehensive. It does not define everything (e.g. offer) and some provisions only apply to "merchants." Any gaps in the UCC are filled by common law principles (in this sense, common law applies to "everything else.")
Unless your prof requires it, you shouldn't need to cite cases.
I hope that made sense. Contracts was a while ago so if I am wrong, I hope someone will correct me.