Looks are probably the first thing that you would look for. At the very least you will have to look at your case, so it should look good. Many cases, even really cheap ones can come in many different colors and styles. Of course looks are important, but that is an easier thing to decide than the more unseen details that can effect the design. We will look at those in details, so that apart from a good looking case, it will be functionally good too.
Construction of the case will mean the difference in how much of a beating the case can take, how sturdy it is and how easy parts are to put in. Most cases utilise aluminum of thin steel. Very cheap cases that use aluminum are often very flimsy because the aluminum is more expensive and so they keep costs down by making it thin. Under $50 don’t expect much. Might be fine if it’s never transported or knocked. More expensive cases for $150 and up are aluminum. They are constructed from tough, thick aluminum, because of this, they are heavy, which is an easy way to tell if its strong or not. Avoid aluminum, except for more expensive cases.
Fans on the case keep air flowing through the computer, pushing cooler air into it and sucking the warmer air created by the CPU and other parts out. Modern computers have become hotter as they’ve become more powerful so they need more air passing through. Unfortunately the answer of more fans makes more noise. Cases can often take up to 4 80mm fans. This will provide enough air going through. Sometimes you can use less, if not none, for underclocked or light load computers. An option that I like is 120mm fans. They move twice as much air as 80mm fans, but with the same noise, to 2 120mm fans will move as much air as 4 80mm ones, but produce half the noise. Cases need to be made to take 120mm fans or modified yourself.
Thumb screws instead of screws that need a screwdriver are a cheap extra, but can make the opening of the computer that much less hassle, requiring one less screwdriver to be used.
Another extra to be considered are mounting brackets for hard drives and optical drives. Instead of having to open the case to take out the drives, brackets are included. The brackets are attached to the drives with the normal screws and then the drives can be slotted in and taken out without tools. Useful if you take them out a lot, I don’t, so it’s not high on my priority list.
Something that effects convenience is the positioning of the USB ports and sound plugs. There are always the standard ones on the back of the computer, but the other ones on the case can be just about anywhere. Most common is on the front, but there are some that position them under a flap on the top. On the top is okay, but if your case is in a closed area with something over its top they will be inaccessible. See if the position in convenient for where you will keep your computer.