Two Dogmas Of Ski Poles
Yes I made a subtle reference to Quine's "Two Dogmas of Empiricism" there, but the debate here isn't the analytic/synthetic distinction, but the cheap versus expensive debate.
There are two distinct philosophies that rule the world of
ski poles. The first is "I know I'm going to break my poles, so I'm going to get a cheap pair that way I won't be out of much money when I replace them." The second philosophy is "I'm going to get a pair of expensive poles so I don't break them."
If you are constantly running into trees, then I could definitely see the appeal of the first mindset... but it leaves me wondering "Why would you set foot on the mountain if you knew you were running into trees?" For the rest of us that avoid trees, we really don't do enough to break our poles as often as we might think.
A better pole will tend to break less then a cheaper one, but that's not the main reason why you buy a better pole. You get a better pole because it's lightweight, has a better tip, is stronger, and has a better grip (which, believe it or not, is a darn good reason to upgrade). For example, I have a pair of Scott A-12 composite poles, I bought them because 1) they had a grip that actually fit my hand, 2) they had a nice padded wide strap, 3) their tips held pretty well on ice (admittedly, not as well as my racing poles but I'll explain why later) and 4) the shock absorption characteristics of their carbon fiber helps keep me from getting the skier's equivalent of tennis elbow. It's true that because they are slightly flexible, I can bash them against trees and they can absorb a healthy amount of impact (where an aluminum pole would dent or bend), but that was one of the last of my considerations.
If you want to save money and that's your primary consideration, by all means go for a cheap pair of poles. If you want a better pole because it's more comfortable to hold, is easier to plant, and puts less stress on your body, then go with a better pole.

Materials
AluminiumAluminum is by far the standard material to make poles out of, because it is cheaper to make and it is lightweight. However, there is a big difference between different kinds of aluminum. A stronger aluminum alloy can be made into a thinner (because they don't have to use as much material) and stronger pole. A stronger pole will give the user more "bash resistance," and a lighter and thinner pole will put up less wind resistance, be easier to carry, and be easier to plant.
Because aluminum is so stiff, it makes for a much better pole plant on ice because all of the user's energy can be used to stick it in place. This can be good and bad. It's good because you can get sharp, precise pole plants and your pole won't tend to slip as much, but bad in the fact that it translates every shock from every pole plant straight up your arm.
Carbon FiberCarbon fiber is a lightweight, but sometimes expensive, alternative to an aluminum pole. Its key attribute is its flex. It acts as a shock absorber every time you make a pole plant, and because it flexes so much, it has an increased amount of durability. Hits that may bend or dent an aluminum pole may be absorbed in a carbon fiber pole instead. Its only downfall is that if you place it on ice, sometimes it can vibrate or move around some.

How To Size a Ski Pole
Alpine PolesWhen looking for the right size pole, simply turn it upside down and grab the pole just under the basket and look for your arm to make a 90 degree angle at the elbow.
As a general rule of thumb, this sizing sizing chart works pretty well:

Nordic PolesNordic poles are much longer than alpine poles so that the skier can get an increased amount of thrust from each pole plant. A skate pole should measure somewhere between your lower lip and your chin, while a striding pole is slightly shorter and should come up just under your armpit.
Touring PolesAT and Touring poles are telescopic so they can be adjusted with changes in slope. Therefore, lengths aren't as critical to this type of skiing as nordic or alpine poles.