Hmmm I guess it really depends on what you want to go with, prefolds and wraps are your cheapest option BUT you have to change really often, especially with a toddler and it can be hard to get a good fit (unless you just fold and lay in the wrap) with a wiggly toddler. If I were you I'd get a bunch of pockets which for good ones range from about $17-25 each. But if you buy in bulk, like larger amounts at once they will give a discount. I think you could do with a dozen if you wanted to wash every other day, but I really think I'd go for 2 dozen to be sure you have enough. Probably a few hundred dollars. You can get 12 Fuzzi Bunz for $203. You could always mix and do those with a dozen of prefolds too, and use both, a dozen prefolds would only be about $25 give or take a few dollars depending on the size.
The washing really isn't too bad, depending on how many you have it can add an extra 2-4 loads a week, but still not bad. I just keep mine in a trash can with a pail liner, toss them in, then dump into the washer, do a cold rinse then a hot wash with detergent then another cold rinse then dry
