My favorite book right now on representation theory is Claudio Procesi's Lie groups: an approach through invariants and representations. It is one of those rare books that manages to be just about as formal as needed without being overburdened by excessive pedantry. He gives a rather complete picture of both compact and algebraic groups and how they interplay, while doing a nice job of explaining the necessary background in algebraic geometry and functional analysis. He covers all the "standard" material on Young symmetrizers, Schur duality, representations of GL_n, semisimple Lie groups & algebras, as well as more advanced stuff like Schubert calculus and some basic geometric invariant theory. This book was the first place I started to feel like I was "getting" the big picture, after picking up bits and pieces from different places.

If your institution has a subscription to SpringerLink, you can probably download this book for free (legally) and purchase an on-demand print version for around $25 USD.

Since this question was about a "learning roadmap," and not just for a single textbook, let me mention my favorite book that fits in your back pocket: "Lectures on Lie groups and Lie algebras" by Carter, Segal and Macdonald. The section by Segal is especially nice.