There's always the classic Abstract Algebra by Dummit and Foote. Section II of the text gives a nice treatment of ring theory, certainly providing plenty of review for what you have already covered while introducing more advanced concepts of ring theory. Section III will cover the field and Galois theory you're interested in. Some of the exercises can be difficult at times, especially for self-study, but the authors tend to give a number of examples and always provide the motivation for why they are doing what they are doing.
Cassels and Fröhlich is still the best reference for the basics of Class Field Theory, in my view. Cox's book, recommended by lhf, is also a good place to get motivation, historical and cultural background, and an overview of the theory.
Also the article What is a reciprocity law by Wyman is a helpful guide.
The key point to grasp is that there are two a priori quite distinct notions:
class fields, which are Galois extensions of number fields characterized by the fact that primes in the ground field split in the extension provided they admit generators satisfying certain congruence conditions (e.g. the extension $\mathbb Q(\zeta_n)$ of $\mathbb Q$, in which a prime $p$ splits completely if and only if it is $\equiv 1 \bmod n$); and abelian extensions, i.e. Galois extensions of number fields with abelian Galois group (e.g. the extension $\mathbb Q(\zeta_n)$ of $\mathbb Q$, whose Galois group over $\mathbb Q$ is isomorphic to $(\mathbb Z/n)^{\times}$).
The main result of class field theory is that these two classes of extensions coincide (as the example of $\mathbb Q(\zeta_n)$ over $\mathbb Q$ illustrates).
This fundamental fact can get a bit lost in the discussion of the Artin map, idèles, Galois cohomology, and so on, and so it is good to keep it in mind from the beginning, and to consider all the material that you learn in the light of this fact.
As for a more general road-map, that is a bit much for one question, but you could look at this guide on MO to learning Galois representations.
Best Answer
Macwilliams and Sloane's The Theory of Error-Correcting Codes is excellent though its about 40 years old at this point, but everyone who is serious about coding theory needs to own this book.
A book I quite like that's more recent is R.M. Roth's Introduction to Coding Theory -- has a bit of a CS flavor to the approach. For engineering (esp. applications), I think Error correction coding by Moon is good.
For LDPC codes and the like, Richardson's Modern coding theory or Mackay's information theory book are good points to start from.