I second Cassandra's advice. In addition to all she suggests, I say get a clothes wringer. (Cassandra does it the old fashioned way like my grandma, and the clothes really do turn out good). The wringer is a good investment for anyone if for some reason the power goes out, or you truly just want to avoid using heavy appliances like the washer and dryer.
For us, the wringer made all the difference in the world when we don't use the washer and dryer for whatever reason. Especially during the winter months when you can't take things outside because they'd freeze. Though I do know someone who hangs stuff on clotheslines outside in the winter. While still stiff/frozen, they press the clothes with an iron on the dry heat setting, right after bringing the clothes inside (before they thaw) and in no time (so they tell me) the clothes are dried and pressed! I've never tried it, so I don't know how they're able to do this without problems.
Anyway, if you have a really moist basement, you may run into moldy clothes! With a good, heavy duty wringer, you will get your clothes pretty close to dry, cutting down on air drying time. You can buy the wringers at Lehmans.com or do a search on the internet and price check around. They screw/clamp on the the side of any steel washer tub or even the tub in your basement.
The wringers are powerful enough to squeeze water from a big comforter, but gentle enough to run a cashmere sweater through if you were into handwashing fine garments.
If you have a safe heat source (not a space heater or anything that could be a fire hazzard if the clothes fall on it) such as a woodburing stove or fireplace, you can take advantage of that dry heat and put your clothes drying rack in the room near by not next to the stove/fireplace. That speeds things as well, and also helps with the stiffness issue.
Lastly, I've found very well made but cheaply priced drying racks at IKEA. If you can't get to an IKEA store just go to their website at www.ikea.com. Lillian Vernon has some good laundry extras too, such as retractable wall drying racks, mesh drying shelves for sweaters, and more. Go to www.lillianvernon.com.