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Taken from the International Rules for Underwater Hockey, 8th Edition:
“Each player shall be equipped with a mask, which must have safety glass or other safety material fitter; a non-metal, pliable snorkel; a pair of conventional underwater hockey fins (made of rubber or other non-dangerous pliable synthetic material, excluding fiberglass) which is approved by the CMAS Underwater Hockey Commission; hand protection for the playing hand(s), and an underwater hockey stick. Head Caps with firm polyethylene or rubber ear protectors must be worn.”
The mask must be a dual lens mask unless it has a center divider/support that is part of the frame of the mask. You want a low volume mask, both for visibility and to decrease the chance of it flooding if it gets bumped. A low volume mask also will provide less drag underwater, increasing your speed.
The most important thing is to get a snorkel with a soft mouthpiece so it doesn't hurt your teeth if it gets hit. Purges are fine; just make sure they are soft purges. Don't spend too much money on the snorkel as most players end up cutting the top 2-3" off of the snorkel to reduce the drag and make it easier to clear. Some of the really cheaper snorkels from Sports Authority and similar places are too constricted for hockey. Make sure you can fit your thumb into the top of the snorkel; otherwise the opening is too small. Make sure that the inside of the snorkel is uniform and doesn't have a connector that constricts where the two parts join. Another good idea would be to get a snorkel with a slender profile to reduce drag and vibration.
Hand protection must not contain rigid or sharp reinforcing material. Gloves used for hand protection may not have webbing between fingers, or be of any design that would aid in swimming. Other than that, glove design is pretty flexible. You can make your own glove, or you can buy a glove from a bunch of different places. Most gloves are cloth layered with silicon rubber, but some people use nothing but electrical tape and other similar materials to create custom, lightweight gloves.
If you are going to pick one area to spend the extra money and get quality gear this is it. There are lots of different makes and models of fins out there but many of them do not work for Underwater Hockey.
You definitely want to get full foot fins vs. the
scuba type. The short swimmer's fins and really long free diving fins
good for underwater hockey.
Other than those restrictions, stick design is completely up to the player.