The first thing to understand is if you have a mold and mildew problem just killing the mold will not (I repeat, will not!) solve your problem. You can use as many mold killing products and call as many mold remediation professionals as you want, but unless you fix your moisture problem in your basement the mold and mildew will keep coming back.
If you have any existing mold, you need to safely get rid of it before you do the work to prevent it. There are hundreds of types of mold and not every single one is toxic; however, every type of mold can cause its own problems. Breathing in mold spores of any types can cause or exasperate allergy symptoms, asthma and other respiratory problems. The existing mold is what causes sick building syndrome where people get itchy eyes, scratchy throats, and coughs just by living among mold.
Mold should be removed by a professional who uses professional-grade products. Once the existing mold is gone—and we mean completely gone—then you need to install and basement waterproofing system and possibility a dehumidifier, fix any leaks and control all the water to then prevent the mold from returning.
Truly killing basement mold is about removing the sources that mold needs to grow. Mold is alive, eats, and grows. The colonies flourish in environments where there is water and food. Mold loves dark, warm places. If you can see visible mold it usually means it started somewhere darker and deeper where you can’t see. Mold loves to grow under the carpet eating away at the carpet pad or behind the walls feasting on the fiber pad insulation. That is the reason the EPA steers homeowners away from using carpet and bat insulation in the basement.
Look at the mold growth as a symptom to a greater issue. Treat the cause and control the environment to truly kill your mold problem. If you control the environment and eliminate the water and/or any food sources for mold (i.e. sheetrock, carpet, insulation, etc.) you will ultimately beat the mold.