Vinyl Storage

It would have to be really humid to have any effect on the outer jackets or sleeves. The only concern I would have is flooding, a friend of mine just had a bunch of his albums get soaked. The vinyl was fine but the jackets are toast, maybe toast is a bad choice. But ruined is accurate. 

Does the basement have a sump pump? If not, maybe raising the shelves up on 4x4s could help prevent flood damage. 

Just put a portable dehumidifier in the room and set it to run automatically and have zero worries. Keep the albums 12 to 18 inches or so off the floor . (cinder blocks)
You have to be vigilant to keep mould from getting in the cardstock of the sleeves, and the paper inner sleeves then migrating into the grooves. I have over 8000 stored in the basement and have for a couple decades like this with out issue. It doesn’t have to be really humid as posted above. Its the CONSTANT accumulation over time that makes things musty/mouldy quick. Cheap dehumidifier is pretty inexpensive insurance and up off the floor will save from the rare and off chance of a foot of water in your basement should you not have a sump pump or it fails to start. Many people never check them and just assume they are in working order.