Sometimes referred to as "sweaters", the jersey is more often made of a light mesh. If you join a league, you'll usually receive a jersey (stitched with your name on the back). This will be part of your uniform. When I played scrimmages, I had a plain white mesh jersey, but my wife had also given me a jersey from Boston University. For pick up or practice games, your coach or team captain may distribute "pinnies", a small mesh coverall that you wear over your jersey so you can temporarily match your teammates.
One other consideration is whether you'll tuck your jersey in your pants or not. Some players sported the "tuck one side of the jersey down my pants" look. I liked this look (the tucked side was my stick side (I was a righty)). Doing this made it feel like my jersey wasn't interfering with my shooting. I needn't have worried!
Finally, if you get named to be a captain, or an assistant captain, you'll have a "C" or an "A" to stitch to the front of your jersey. I was an assistant captain, and for the stitching, I went to a local sporting goods store to have it done "right."