Hi D.,
It's wonderful that you'd like to cloth diaper your next baby. I think you'll like them, I certainly prefer them to disposables! I've cloth diapered both of my daughters and will my next baby due in June.
The least expensive way to go is to use DSQ CPF's (Diaper Service Quality Cotton Prefolds) with covers. The DSQ CPF's cost about $24 a dozen. Diaper covers with snap or velcro closures cost anywhere from $8 - $20 depending on style, brand, material/fabric. Pins are unnecessary, velcro/snap covers hold the diaper in place or you can use snappi clips (plastic clips with teeth that grab the fabric). 2 - 3 dozen diapers and 5 - 6 covers should be adequate.
A full load of diapers is 24 - 30 so having 3 dozen gives you a few diapers to use while the others are in the wash. Newborns use about 12 diapers a day so if you have only 1 - 1 1/2 doz then you'll need to wash every day. If you have several dozen you'll want to be sure to wash at least every 3rd day to reduce stains and odor. Bleach isn't necessary, it reduces the life of the diapers, and can be harsh on sensitive baby skin. As long as baby is exclusively breastfed there's no need to dump diapers in the toilet, it will all come out in the wash. If you begin to get stains sun drying will remove them. Diaper covers can be rotated for several uses when wet and be washed with babies regular laundry.
A more expensive and popular cloth diapering option is to use "Pocket Diapers" or "AIO's" (All-in-ones). Pocket diapers like Fuzzi Bunz, Bum Genius, and Happy Heineys are made of two layers of fabric. The outer fabric is waterproof PUL (polyurethane laminate) and the very soft fabric next to baby's skin is micro fleece that wicks wetness away from baby's skin. Between the two layers (in the "pocket") you place an insert usually made of micro terry but regular cloth diapers can also be used. Pocket diapers and AIO's are very easy to use. Some daycares will use them because they are as easy to use as disposables. Dad's tend to like them too. These diapers are around $20 each and most come with an insert.
Some diapers come in sizes: small, medium, large, etc. Other diapers are OS (one size) meaning that they have size adjustable snaps and are meant to fit babies from 8 - 35 pounds. The OS option should save $ since you don't buy new diapers each time baby changes sizes.
I do not have problems with leaks, even overnight, for heavy wetters you can add a doubler or second diaper. I do not find washing diapers a hassle, in fact it's quite easy since there's no laundry sorting required and no folding required either just use them straight from the clean laundry basket. Cloth diapres are cheaper than disposables in the long run but a big expense all up front. My advice is to use the next 4 months to set aside the $ you'd normally budget monthly for disposables. You can either buy all your diapers at once or spend the diaper budget monthly to buy some of what you need until you have a full stash. Good condition second hand diapers can usually be sold for about 50% their original cost through Craigslist or second hand baby stores.
There are many options for diapering. Check out www.pinstripesandpolkadots.com for some great articles on the "myths" of clothdiapering as well as tips and suggestions for getting started and the differences between diapers and a laundry detergent comparison chart. www.sahmdiapers.com is a good site for inexpensive diaper covers and fitted diapers. I like www.kellyscloset.com for good deals, she often sends free shipping coupons by email.
I wish you the best as you figure out the clothdiapering system which will work for your family. There is a lot of information available and I hope you get what you need without being overwhelmed. Please let me know if I can help any further. Best wishes, K.