A casement is a window that is attached to the frame on the side with one or more hinges. They are more air tight than double hung windows due to the door like construction. The windows are often operated with a crank or lever.
A double-hung window is one that has two sashes that are able to move up and down. These windows are harder to make air tight due to the connection when closed between the top and bottom sash.
Windows can be made of vinyl, fiberglass, or wood. There can also be combination materials such as a fiberglass clad wood window. These are wood on the inside and fiberglass on the exterior.
Some of the qualities that should be looked at when selecting a window is the Design Pressure, U-Factor, and Solar Heat Gain Coefficient.
Design pressure rating measures the amount of pressure a door or window will withstand when closed and locked. The higher the DP numbers the better the performance.
U-factor correlates to the rate of heat transfer. The lower the number the better a window is at keeping heat inside the structure.
Solar Heat Gain Coefficient measures how well a product blocks heat from the sun. In warm climates, the lower the number the better. In cold climates you want a higher number to allow the heat into your structure.