Unless you are very short on space in the basement, I would suggest that
you get a medium sized humidifier on wheels designed for a few rooms.
You also will need a cheap device to measure humidity. Then you just
adjust the humidity control on the unit until you get the humidity you
want. You can get such units at Sears for under $US 100. Actually they
do not cost much more than the tiny table top units. The larger the
water capacity, the better, so you do not have to refill so often. I
have had a Sears humidifier set at 70% RH for several years in my wine
room, and I only have to refill with water once a week and change
filters now and then. I use much more water in the summer than the
winter, because the air conditioner that keeps the temperature at 55 F
removes much moisture from the room. Be sure to use a humidifier
bacteriostat in the water, as some rather nasty microorganisms sometimes
will grow in the water, be blown out with the humidified air, and cause
health problems for some people.

In fact, I would first measure humidity for a while. It could turn out
that you do not need a humidifier. Probably 50% RH or higher woud be
safe for most wines even for long storage. For short term storage, even
a lower RH might be tolerated. If you go to too high a RH you may
develop a mildew or mold problem in the basement. This will not hurt the
wine, but it may ruin the labels as well as other items you may have
stored in the basement.

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