Finding the best route for your family can take some research, whichever path you choose, here are some tid bits to get you started...
Cloth diapers are reusable and can save money in the long run if you plan ahead. BabyWorks, located in NW Portland, has a cost analysis (see page 35) of cloth versus disposables as well as a lot of other helpful information about washing, preventing leakage, etc. If you have enough on hand, it will save you in laundry, but the initial costs up-front can be high. You can also use a diaper service such as Tidee Didee. There are many types of cloth diapers and accessories available; Baby Works and Milagros both carry a wide selection and both have expert knowledge to help you navigate the product decision-making process. There are also a lot of local mamas who make cloth diapers and sell them, that is how Cynthia Thompson started Zoom Baby Gear in N Portland.
Many people sell their used cloth diapers at local shops such as LilyToad and Milagros (and the new Queens Mab, I believe, is planning on taking them). You can also find used cloth diapers on Craig's List, Urban Mamas Exchange, Mothering.com Trading Post, Diaper Exchange, Orange Star Fish, and E-Bay. With Craig's List and Urban Mama Exchange you have the advantage of being able to see the diapers before buying them. Be sure to check the integrity of the fasteners, lining, and elastic leg bands.
If you are interested in cloth diapering but do not have the financial resources available to get started you can put the diapers and accessories on a gift registry or wish list, ask friends to pass theirs on, and/or encourage local nonprofits to start a donation or exchange program. As Nurture grows, this is one project we plan to start, but for now you can look into programs like Miracle Diapers, Lend a Hand Diapers, and Grandma Jacquie's Diaper Barn, which are all nonprofit programs that help families with financial constraints get cloth diapers.
Like cloth, there are many brands and styles of disposable diapers on the market. If you are looking for chlorine free diapers Seventh Generation and Tushies are both options and can both be found at New Seasons. There are also Huggies, Pampers, Luvs, etc. which can be found at most grocery stores, Target, Fred Myers, etc and some of the stores also carry generic store brands. For good deals, look for sales and coupons. Target often has good sales on disposables.
For information about EC visit Diaper Free Baby. There is also a local group Oregon Diaper Free that shares resources, ideas, support, and education about EC and has regular get-togethers. Heather Caliri has an essay about her adventures with EC titled, Relieving Myself, in the Winter 2008 issue of Brain, Child.
There are flushable diapers liners and flushable diapers.
Flushable diaper liners are used with cloth diapers and they basically make cleaning the solid matter (poop) from the diapers easier (not used to increase absorbency). For newborns and small babies you can cut the liners in half to save. Some brands hold up okay if they are washed in the washing machine and can be reused (wet only, not if they had poop), but that is not how they were designed.
g-Diapers are the only flushable diaper system on the market, that I know of, right now. They use a diaper cover ("little g pants") and a flushable refill. If you cannot flush them, the wet ones can be composted.
Some families choose a combination of diapering strategies or use a certain type when they travel or at night. There are so many guides and resources on the internet that it would be difficult to list them all, but you can do a Google search for more information. Good luck!