There is really no way of being sure you bought the right stuff without demo-ing the gear first. Most outfitters have what they call demo days. A demo day for ice climbing equipment may be hard to come by, but could prove to be invaluable in the purchasing process. Check at your local outfitters to see when their next demo day is. Some stores also allow you to test the equipment by renting or just using the gear for day (private demo). Retail stores like REI And EMS have demo days, so give them a call and set up an appointment.
If you have a friend who can kind of show you the ropes that would be beneficial as well. This way you can bang on your friend’s equipment and really give it a hard test without feeling bad.
Ice climbing is a super technical sport whether you are simply mountaineering or scaling up an ice column. Never climb alone, especially when elements are part of the equation. Always have a buddy along and do yourself a favor and take that mountain navigation course that your local outfitter is giving. Getting caught in a whiteout could end more than your climb. Be sure to use your head when getting the gear you need; ask tons of questions and when in doubt, pay a little more for the best stuff. After all you life may hang in the balance.