On more than one occasion, I've been asked exactly what you need to go ice climbing. It's not terribly difficult to obtain, though it can definitely be a big investment. Equipment that's meant to keep you alive isn't something you skimp on unfortunately....
Fortunately for you, demo gear is available if you get there early enough... and I do mean get there EARLY.
Try new things and learn what you like, especially:
Ice Tools
Crampons
Boots
These are the three single most expensive items you would purchase, aside from rope.
Here are some of the items we use, then a little explanation after the list.
I can say this not being a professional to any extent, though what I can say is that I've been several times now and learned from what I did wrong. For instance, packing 3L+ of water in, and packing a 3L ice cube out is no bueno.
Climbing Equipment:
Backpacks 38-60L should do the trick. Ice tool mounts are huge.
Ice Tools (2) Required (no adze recommended)
Helmet -Required (rock/bouldering/canyoning helmets will work)
Crampons (2 ) Required
Belay Device Required
Harness Required
Back Up Belay -Recommended
Locking Carabiner 1 Required, 2 recommended
Rope? Not needed if you're taking clinics and seminars
Ice Screws? Not needed if you're taking clinics and seminars
Small First Aid kit Recommended
Small Waterproof box (for your phone)
Ice Tool Clips Recommended
Clothing:
Base Layers - short sleeve and long sleeve
Insulating Jacket Layer
Outer jacket Shell
Flexible Adventure Pants
Long Underwear / tights
Skull cap
Insulating Beanie
Stretchy Ice Climbing Pants
Medium Gloves - water resistant
Thin Gloves
Belay Gloves (optional)
Camera Stuff:
Olympus Tough Smart
DSLR with at least an 18-55mm and a 70-300mm. Tulip hood is good for dealing with the snow.
Camera Cleaning kit
Tripod
GoPro Hero 5 Black + Session - Helmet mounts, hand mount if you want to get kooky.
Karma Grip is pretty schwifty for walking around or rappelling.