First off activated carbon will NOT negatively effect a planted tank.
Activated carbon is used to remove larger molecules from the water column. Many of these molecules can give off a swampy smell and cloud the water.
Many people worry about the activated carbon removing the nutrients from the water column as well. This is not a problem because of how the activated carbon works.
Activated carbon has tons of microscopic pores throughout. The size of these pores determine what size molecules it can remove. Basically the molecules are too big to fit through the small hole and get jammed in the pore. How the carbon is manufactured determines what size of molecule is trapped. There are some commercial grade activated carbon that can remove very small ions. However, aquarium carbon is designed to remove only the larger molecules. The smaller ions flow freely through it.
It is a very effective mechanical filtering mechanism. It is much more effective in straight mechanical filtration that any other media. It also works effectively for biological filtration as it has a high surface area. In my 125 gallon tank the carbon generally last 4-6 weeks.
As to the cost of using it - don't buy the little pre-filled pouches. They are way overpriced. Just buy the loose carbon and either place it directly in the tray or make your own pouch (paint strainer bags work well).