I've owned three portable dehumidifiers over the years, and they've all been a pain in the ass. I've still got the last of the three, but instead of using it right now it's in the storeroom.
If you're willing to put up with a few things, they'll definitely suck the air dry and cut down on mold. Here's what you've got to put up with...
1) heat... lots of it. I tried to use one to keep the bathroom from fogging up and growing mold, but it also warmed it up in there. The humidity would make you sweat, but so does the heat from the thing. I'm in Florida, so this is a real bitch in the subtropical climate here.
2) de-icing. The heat from the dehumidifier might be a plus if you're in a colder climate and the room you're going to put it in is chilly anyway, but the trouble is getting the room up to temperature so the coils don't ice up. Get one with an automatic de-ice cycle.
3) cleaning the coils. You've got to do that every couple of weeks. I'd recommend getting a scrub brush just for the dehumidifier. If you can get one with an air filter, that should help keep the coils from clogging up with dust and lint and crap.
4) emptying the bucket. Most dehumidifiers have a connection for a drain hose, and if you're lucky, you can find a place on a shelf where you can run the drain hose by gravity into a sink. That condensate gets really nasty, by the way, so don't try to re-use it for anything. If it's on a shelf, you still have to make sure it's got room to circulate air and vent off its heat, and also that it doesn't "walk" off the shelf due to its own mechanical vibrations and crash onto the floor.
The above tips apply only to the portable, refrigerant-type dehumidifiers. You mentioned you've got a two-story house. Is the dehumidifier for the entire house? If so, you might want to invest in the kind that hooks up to your central air system.
As for the dessicant kind... Are you talking about Damp Rid and similar systems you can get at the grocery store? Those make a nasty chemical goo that you've got to empty out periodically, and are really just for confined spaces like closets, cabinets, etc.
Hope that helps.