For me, getting involved in Zen practice has involved a lot of reading to help myself get up to speed reasonably quickly. Here's my suggested reading list, in recommended order (which is not necessarily the order I read them in):
Suzuki Roshi
Zen Mind, Beginner's Mind (kindle)
The Classic. Required reading if you're planning to practice at Zen Center. Seriously, if you're reading this blog and haven't read this stop right now, got get a copy and come back when you're done.
Zen is Right Here: Teaching Stories and Anecdotes of Shunryu Suzuki (kindle)
A collection of short, easily digestible, quotes and anecdotes of Suzuki Roshi. A good one to have handy for idle browsing or if you want a quick something to ponder.
Crooked Cucumber: The Life and Zen Teaching of Shunryu Suzuki (kindle)
Not by Suzuki Rosh, but an account of his life and the early years of SFZC. Full of stories that really help to make sense of some of the particularities of life and practice at Zen Center. My favorite is about how the first rule at Tassajara is that brooms should be stored with their bristles up, and every time I've opened a broom closet (which turns out to be a lot) I've found them stored just so.
Not Always So: Practicing the true Spirit of Zen
Another collection of Suzuki Roshi's talks. It's only available in print right now so it might take me a while to get around to finishing.
Branching Streams Flow in the Darkness (kindle)
Some of Suzuki Roshi's last lectures, discussing the Sandokai which is chanted on a regular basis in services, and particularly during memorials. I'm about half way through so that the first half of the chant is filled with meaning and the second half is still a bit of a mystery.
Reb Anderson
Reb is the most senior teacher at Zen Center and lives at Green Gulch. His two books cover the precepts (which you'll want to read before asking to take the precepts and getting permission to start sewing a Rakusu) as well as a collection of Dharma Talks he's given over the years.
Being Upright: Zen Meditation and the Bodhisatva Precepts (kindle)
Warm Smiles from Cold Mountains: Dharma Talks on Zen Meditation (kindle)
D.T. Suzuki
D.T. Suzuki is a well regarded Buddhist scholar who wrote some of the first english texts on Zen. He's primarily concerned with Rinzai but these texts are what brought a lot of people to Zen Center in the 60s and 70s so they're helpful in understanding the early history of the lineage and some of the details of practice.