Well, I guess meditate on the laundry thing some more. If you have your own laundry machines and can do a wash anytime, then no problemo. If you have a shared laundry and would be running the risk of other people moving your stuff around or seeing what you're washing, then cloth might not help you much with your privacy. It might make things worse, actually. But if you can get enough cloth diapers to meet your demand, then you'd probably be saving money pretty quickly.
A lot of people think, "I'll just wash these cloth diapers by hand and hang them up to dry," but--these things can take a looooooooooong time to dry, especially indoors on a rack, and especially if we're talking the all-in-one styles. I'm talking several days. Plus they get kinda stiff that way. Tumble-drying diapers is not only a gazillion times faster, it also softens them. So I guess my advice would be: Don't get into this thinking you'll be hanging your diapers up on a rack to dry. They'll dry so slowly that you'll need to buy three times as many to ensure that you always have dry ones ready.