In the central Pacific, a little near the equator, right at the surf line (~100% humidity all the time with salt spray) for buildings containing delicate equipment we used a combination of refrigerated air conditioning and small portable dehumidifiers (appliances that use refrigeration to turn electricity into water
). Everything had filters changed regularly. If the outside environment is humid, refrigeration is usually the only effective way to get rid of humidity. In my experience (I hate Florida for this reason) the only way to get rid of mold/mildew is to rip out and discard the affected material and/or scrub down the material that can take the chemicals with a disinfectant.
Make sure your new house is being built properly with moisture barriers in the right places, moisture permeable air infiltration barriers in the right places, an appropriate HVAC system with enough fresh air exchange, proper ventilation of non-living spaces (attic, crawl space, etc), proper drainage and a sound roofing system .