Another piece of equipment that's a must. I've seen many beginner players jump on the ice without other pieces of equipment, but forgetting these is bad news, simply because you will fall down on the ice, and falling down on unprotected knees repeatedly is not healthy.
The protective casing for the knee is sometimes made of a gel, and in my first pair of shin guards, this gel leaked out, resulting in a less comfortable case (the stiff shield protecting the knee still worked). I ended up buying a pair with a more rugged design.
Most knee/shin guards have straps that lock the guard firm against your lower leg. Nearly every player I met (including myself) wrapped the top part of the guard around the knee using some kind of medical tape or velcro strap. This is to better keep the guard in place.
When I stopped playing, it was this piece of protection I missed the most. Ice skating in public sessions can still bring the occasional fall, and falling on the hard ice on my unprotected knees always left a bump or a bruise.