there are tons of different types of filter media available. And it can be quite confusing for the new commer in the hobby. Basicly there are three main types- Mechanical, Biological and Chemical. Out of the three, the chemical is the most useless unless you have a specific reason for needed it. The fish two should always be used in a tank, and at times they can be one in the same.
Mechanical filter media is what traps the debris, waste matter and other physical particules that are in the water.
Biological filter media is media that has a large surface area, but allows water to flow fairly freely though it. This is where the bennificial bacteria colonize and break down waste from the fish that is in the water. This process is called the Nitrogen Cycle. When people refer to a tank being cycled, this is what they are refering too. If enough of the good bacteria are in the tank to keep up with the waste that the fish are excreating to keep the ammonia and nitrite levels within acceptable ranges. But the bacteria do not live on the biological filters alone, as they are found on every surface of the tank. The bennifit of haveing a dedicated bio-filter is so that you can have a higher concentration of this bacteria and therefore a more stable tank.
Chemical filtration is when a substance (normaly activated carbon) is used to remove any chemicals that may be in the tank. This is rarely needed despite what we may hear in our LFS. The most use out of this type of filtration is after medicating a tank for sickness and you need to get the rest of the meds out of the water.
The type that is best depends on the tank. What types and how many fish you are wanting to keep are the big factors. If your going to keep lots of small fish, then you aren't going to need as much as you would if you were keeping larger fish.
Personaly I use polyester filler that I pick up in the craft section of Wal-mart. It's a lot cheaper that trying to buy the pre-made filter cartridges, and works just as well. It does take a little extra time to prepare it for use in a filter ( just cutting the pieces to the proper size), but for the money I've saved it's worth it. I may go though a bag about once a year. If you do use this just make sure that it doesn't have the chemicals added that prevents mold and mildew. It should say on the bag if it does or doesn't.
-HTH