Do you have forced forced air Heating/Air Conditioning?

If yes, install a cold air return in the basement. This will circulate the air, dehumidify it during hot weather and remove the stale musty odor. If your basement is exceptionally damp, a dehumifier would be a good investment too.

I have no knowledge on Humidex or any other ventillation system but I believe their worth would be more for hot-water heat where there is no way to recirculate air trapped in the basement. Bringing air from outdoors to the basement will cool it thereby increasing the relative humidity. You need to extract the moisture.

If you do not have a humidifier, one may be necessary for the winter. Depends on your climate.

I have heard that old fashioned ceiling tiles can retain odors and grow mold - if you have those down there, you might want to replace them with new vinyl ceiling tiles. New Ceiling Tiles has a big selection and they also sell rust proof grid.

Here is a link that might be useful: NewCeilingTiles.com

For my house, I first used a humidity meter- Walmart,. Radio Shack. Humidity was in the 70 -75% range, Now use two dehumidifiers- one in each end of the basement- with controls set to keep humidity about 50%. If basement air is cooler than outside, the basement humidity will be higher- simple physics. The most watertight basements may need dehumidifiers.