Someone just starting out with Batwoman would do well to begin with Batwoman: Elegy. This volume deals with both her then-current interaction with the Religion of Crime, and goes through extensive flashbacks of her childhood and training. Elegy quickly establishes her character, giving Kate Kane both a sense of duty and honor instilled from her upbringing and West Point and the Bat Family drive to combat crime, but also familial tensions that humanize the character. Elegy also stands well on its own, making it an ideal introduction to Batwoman.
After Elegy, her self-titled series is the logical next step. Without any major crossovers with the rest of the Batman Family, Batwoman as a series is basically a stand-alone effort, and thus well-contained. The art is vividly colored, detailed, and very dynamic, and is probably the series' greatest strength, but the writing is usually strong as well, the narrative flows well, and Batwoman stays a consistently engrossing series.
Batwoman's first storyline in 52 is most helpful in showing her relationship with Renee Montoya and the introduction of the Religion of Crime, but her appearance and characterization are somewhat different as opposed to her later stories. She first appears in issue #7, in costume in #11, and is central to the plot of #48, but her appearances tend to be scattered and secondary compared to the other superheroes. Elegy does a good job of filling the reader in on what has occurred to Batwoman, so a casual reader need not search out her earlier appearances, but the 52 issues and the storylines like Flashpoint that follow will intrigue someone looking to see how the character has changed over time.