To control the humidity in your basement, you need a dehumidifier that can keep it between 30% and 60%. Not all machines do a good job of keeping the humidity in that range so you should shop around to see which ones have good reviews. (you can find reliable reviews here- Dehumidifiers on Amazon) Reading reviews of each machine that are made by people who have bought them is a good way to narrow down your choices.
The video below also talks about frost control, fan speeds, auto restart, and energy savings features that you might want to consider before buying any basement dehumidifier.