Yes quarantine your fish. When you first purchase a fish you don't know what type of health it is in, what diseases it may be carrying, or what it could possibly pass onto other tank fish. So you place newly purchased fish into a separate tank (quarantine tank) that has things like a filter, some type of cover for the fish to hide (like pvc pipes or fake plants) and a heater / thermometer. You watch your newly purchased fish for about 4 weeks to make sure that it doesn't show any signs of ick or anything else. At that point you can place it in the display tank.
THe problem is people trust stores too much and don't truely understand how to keep fish. You have to realize that fish are living things, and that although they aren't as difficult as children to keep (obviously), you still need to take some measures to ensure your fish's health. When purchasing a fish make sure that it looks healthy, that it eats, and has no signs of stress or disease. At that point you purchase the fish. Some diseases don't show up right away, so it may LOOK healthy, but in reality it could have ick or some other parasite. So you have to quarantine your fish for about 4 weeks to make sure it is truely healthy, otherwise you risk the possibility of passing the disease onto other fish.
The other reason is treatment of the parasite (sorry noticed i'm using parasite and disease interchangably, and they should be
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) usually will kill your inverts and some coral. The best method of killing ick is either copper treatment or lowering the SG of the water. Both will kill off inverts (because ick is an invert).
So you QT fish for two reasons, one to ensure that they don't pass anything along to other fish, second is that if they are sick you can treat them w/o having to kill off your inverts.
I'm not sure why your fish died, really you need to provide more information about yoru tank. Have you cycled the tank? (don't know what the cycle is read the fax page). If you have cycled what are your parameters? (exactly what are AM, NI, NA, SG, PH, Temp). What do you have in the tank? How long has it been setup?
All these questions are possibilities for the actual cause of the fish's death. It could have simply been sick at purchase too. Until we know specifics we really can't help much. I certainly WOULD NOT purchase any other livestock (fish or invert) until you find out why your fish died (at least ensure all the questions i've asked are within reasonable means of measure).