In nearly all of physics you need an application. This is what separates physics from mathematics and makes the former a natural science, while the latter is more akin to philosophy, and not necessarily rooted in the real world. Now you have done classical physics where everything is in the end based on Newton's equations of motion. Given this framework, you take an application, say Tarzan's trajectory as he attempts to swing across a river, and try to figure out what happens.
Statistical physics is a huge subject and it applies to any system which is made up of a large number of smaller parts interacting with each other. It is therefore important that you try to figure out more specifically what you are interested in: You wouldn't want to waste too much of your time reading up on quantum statistics if what you really are interested in is describing the liquid state.
Here are couple of the more recent books, starting from very basic and going up to intermediate stuff:
"An Introduction to Thermal Physics" by Daniel V. Schroeder. This is a rather standard book for a first course on thermodynamics and statistical mechanics. Most of the book is focused on the former, and the latter is introduced through the partition function basics using an Ising model and an elementary discussion about fermions and bosons and their associated statistics. I don't think the book contains anything that you don't need to know, it is fairly application-field agnostic, and from what I remember, the exposition is very clear and everything is made very simple. You will learn what free energy is and how it connects to the partition function.
"Statistical Mechanics: Theory and Molecular Simulation" by Mark E. Tuckerman. This is a recent book that I have not fully read, but I have read chunks of. The exposition is excellent and the connection to molecular simulations is kept very clear. Not the book you might necessarily want if you want to do liquid state DFT, but if you want a comprehensive understanding of how molecules interact and how statistical mechanics arises from those interactions (mainly classical, but also a chapter or two on quantum stuff), I know of few books that I rate higher than this one. This book starts with a thorough review of classical mechanics, thermodynamics and statistical mechanics and goes on to describe some relatively recent advances and how they are actually used in practice in simulations.
Finally, if I recall correctly Coursera/edX and other MOOC sites have recently had courses on introductory statistical mechanics. You might want to look into those venues as well.
To close, "Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more" -- Arnold Sommerfeld, one of the leading minds of his time. I can fully attest to this quote, and I often go from thinking that I comprehend thermodynamics to the realization that even when my models and equations work, I do not fully at a fundamental level understand why.