Tripod legs are usually made of either wood, carbon fiber, or, most commonly, metal. Aluminum legs are fairly lightweight, rigid, and durable. Carbon fiber legs are even lighter, but will be substantially more expensive and won't provide much added benefit to the average aspiring shutterbug. Expect to spend $100 or more on a set of legs that you can take everywhere you go for years to come.
Additional important features to look for are that the legs are independently adjustable so you can level your tripod on uneven ground, and that the minimum and maximum usable heights of the tripod will meet your shooting requirements. Make sure your tripod legs extend far enough that you can look through your camera's viewfinder when using the tripod, without having to bend over uncomfortably. Take note whether the tripod legs themselves extend to this height, or whether the center post must rise substantially from between the legs to reach this height. The higher the center post must extend, the less stable a shooting platform you will have.
Now check the minimum usable height of the legs. Look for a minimum height of less than 18 inches. A low minimum height will allow you to take clear shots from angles most people don't often see. However, you will probably use this feature infrequently, and let it influence your purchasing decision correspondingly.