Dan, knowing your tastes, I think you will like Fulton-Harris very much. However, if I recall correctly, Fulton-Harris does doesn't go into much depth about some important (and really cool) theorems in Lie groups, such as Peter-Weyl and Borel-Weil-Bott. But of course, you can learn these theorems elsewhere.
I think the book "Compact Lie Groups" by Sepanski is nice, and it does cover P-W and B-W-B. I also found this note on B-W-B to be useful in the past: http://www-math.mit.edu/~lurie/papers/bwb.pdf
