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You need all the gear, except for maybe a neck protector. You're taking a risk without one, but it's a risk most players take.

If you're going to invest in anything expensive, buy a nice pair of skates.

You're going to want to try all your stuff on, if you don't have any idea what you need. So I'd suggest buying in store as oppossed to online. If I were you I'd hit up Sport Mart and Sport Chek. Sport Chek is currently having a sale right now. You don't need the latest and most high end equipment, but I'd buy something descent. Online places like HockeyMonkey.com are great, but it might be a little difficult if you have no idea what size or type of equipment to buy. You can buy used, but that's gross. Most stuff doesn't last more than a few seasons of hard wear, so the only thing I'd look at buying used would be the skates.

You need:

Helmet + full cage. If you are starting out, I'd go with the cage, as oppossed to visor.
Shoulder pads
Elbow pads
Pants + suspenders
Shin pads
Socks
Cup
Gloves
Stick (definitely buy this at Sport Mart)
Skates
Jersey

I recently started playing hockey 2 years ago in a similar position to you. You will fall down a lot and get hit by pucks. Buy all the equipment. Even in no contact games there are lots of collisions and incidental contact. A lot of beer league players are dicks too. They will slash, crosscheck, etc.