Frying pans are an essential kitchen tool. It's one of those tools that you use often, so you want to make a wise investment. Cheap frying pans won't do the job well and they won't last. Most of the time when using a frying pan you want to use it over high heat, so you want it really hot. If your frying pan does not have a heavy bottom it won't be able to conduct and even distribute the heat. With these things in mind, there are three types of frying pans I would recommend having on hand: nonstick, stainless steel, and cast iron.
These pans are you want when you are concerned about cleaning the pan when you are done. I always use a nonstick frying pan whenever I am making scrambled eggs. I also steam broccoli in mine.
There are times you want a pan where things will stick to the bottom. If you are browing a piece of meat in a pan and want to make a sauce for said meat, then you will want to de-glaze, which is using a liquid to get everything that stuck to the bottom of the pan off. That stuff on the bottom is full of flavor, so you don't want to waste it. But if you have a non-stick pan you won't have those flavorful bits on the bottom.
Cast Iron is a great choice when you want your pan really hot, like when browing a chunk of meat for a pot roast. The nice thing about cast iron is when you introduce something cold to it, it doesn't lose much in the way of temperature. I have seen people use these pans for making cornbread in, which brings me to another advantage of cast iron, it can take any heat your oven can dish out.
So whatever you choose make sure you are getting a quality pan. Also think about your needs, what are you going to cook in it? There are times when it's nice to have multiple sized pan around. You may not want a huge pan if you are going scrambled eggs for one person. A good frying pan equals a happy cook.