I hope to fill up more of this page as time progresses.
There are at least three books that I would highly recommend to an undergraduate student who may have the requisite “mathematical maturity” but perhaps has not tasted the elixir of Category Theory yet.
Conceptual Mathematics: A First Introduction to Categories (Paperback) - F. William Lawvere and Stephen H. Schanuel.
Sets for Mathematics - F. William Lawvere and Robert Rosebrugh
Topoi: The Categorial Analysis of Logic - Robert Goldblatt.
I intend to write reviews (containing details on each chapter, hopefully) for all the aforementioned books some time in the future. It will be a work in progress.