In order of importance:
Hockey Skates (you MUST try these on in a hockey store or play-it-again sports...You can still BUY online, but you will want to know your accurate sizing) - No toe-picks or hybrid skates allowed for safety reasons.
Helmet with face mask (wire cage, clear plastic, or combo - must cover your whole face and have a chin strap)
Hockey Shin Guards (Probably your most important piece of safety equipment because 90% of falls will be on your knees. Soccer and field hockey ones don't cover knees)
Hockey Gloves (Very easy to buy used ones for these but they do get stinky)
Elbow Pads (I have never found super heavy-duty ones all that helpful. As long as they fit and cover your funny bone you should be fine)
Hockey Pants (The newer they are, the stiffer they are. Make sure you have plenty of room to bend )
Shoulder Pads (We do not play with checking so these do not have to be heavy weight. Just imagine falling down or running into the boards and judge your level of protection)
Hockey Socks (to go OVER the shin guards), practice jersey, some form of garter belt or spandex with velcro to hold the socks up
Hockey Stick - Don't spend an arm and a leg until you begin to know what feels right (or left :-) ). It is very common to borrow one or get a used one at play-it-again until you get comfortable. Women in our league often use an intermediate or even junior stick depending on their arm strength.