Athletic "Cup" and Supporter
This is an obvious purchase. If you've never played a sport that required putting on a supporter, make sure practice at home first. Finally, since it's the first piece of equipment you'll put on during a game or practice, be sure you put it on. I remember at least one player forgetting to put on his cup, and then announcing that fact to the team after he had put on his entire uniform.
Garter
The garter is a strip of nylon with a velcro patch to tie it around your waist. The garter, when put on properly, has strips of fabric that hang from the waist. At the end of each piece of fabric is a metal fastener and rubber "tong" that slide and lock against one another. The intention is to place your hockey socks on top of the fastener, then press the tong on the sock, latching it to the fastener, and holding up your sock. Think of the garter as suspenders for your hockey socks. Make sure to bring two in your bag as forgetting these can make your practice or game frustrating (since your socks will always be falling down).
Undershirts
I've seen the gamut of undergear, from specially made shirts, to plain old tee shirts, to bare skin. I preferred a long sleeve but "thin" shirt, and the only one fitting the bill was a dressy pullover that I would normally wear underneath a sweater to work. After I played hockey in it a few times, it became consigned as my undershirt. I liked the long sleeve because it made the elbow pads and shoulder pads feel more comfortable on my body. See what works for you!
Socks (for Your Feet)
A friend of mine got me into wearing "sanitaries", which are these really thin socks that are meant to be worn under thicker socks. (I believe these are used by baseball players.) The ice skating boot is typically "snug", so having a thin sock allows you better control, plus your foot does sweat considerably while playing.