This section of the tutorials and
Richard Jeffrey, [1967-2006] Formal Logic: its Scope and Limits
would work well together (and it is an excellent book).
You need to know some propositional logic to be able to understand the tutorials to come. In particular, you need to know about the symbols used in propositional logic, truth tables, satisfiability, consistency, and semantic invalidity (by counter example). You do not need to know propositional rules of inference and derivations.