I know this is a very very weird approach, but I suggest you do it this way:
1) The Boltzmann distriution, the partition function along with contributions to the internal energy. (This is unusually hard to start with, but you get an amazing picture of thermodynamics when done)
2) The first law of thermodynamics: Learn the concepts of work, heat, and energy. Use time to discover what kind of works that exists and conclude the first law by learning your self about the state function, enthalpy (H).
3) Thermochemistry - An addition to the first law, read a bit about it and get a intuitive understand using the knowledge from 2)
4) The second law of thermodynamics: Learn the concept of entropy and use some time seeing the relationship between the partition function and Boltzmann formula for the entropy.
5) Concentrating on the system: Learn about the state functions: A (Helmholtz) and G (Gibbs) along with their partial differentials
6) Combining the first and second laws: Derive the Maxwell relations, and try combine the laws to alter the expressions for the internal energy.
I know I totally skip the 3. law of thermodynamics, but I don't consider it that relevant, I think it should just be known and that's it... no need to harder calculations to understand it.