Ice climbing is not as dangerous as it looks. All your gear can be rented from your guide, but here's a pro-tip: schedule your trips during "ice climbing festivals" where you can try all kinds of new gear. There are, of course, different types of ice climbing, (like alpining, mixed, etc) but you shouldn't worry about that unless you plan to go pro.
Heavy-weight merino wool or synthetic baselayer (1 if you run hot, 2 if you run cold). Baselayers are the tops closest to your skin.
Midlayer, such as a sweater or puffy jacket. Down puffy if you run hot, synthetic puffy if you run cold (or if you're a vegan.
Outer layer, a shell like a rain jacket if you run cold and/or insulated, water proof/resistant jacket.
Something comfortable, ideally stretchy and/or durable, that can withstand abrasive rock. Keep in mind you will be in a harness the entire time, so comfort is emphasized.
Sturdy sneakers or hiking boots.
You would also be outfitted with specialized ice climbing boots by our guide if you don't already have your own.
Additionally, you will also be outfitted with specialized crampons that go over your boot.
Winter accessories (see above)
You will also be outfitted with harness, helmet, and ice tools (like ice picks, but awesomer) by your guide, unless you already have your own.