Wow. There are a huge array of diapers!
If you can afford it, and if you're looking for the combination with the least amount of effort (perhaps because it seems daunting, or your hubby is resisting), then I would highly recommend "All In Ones", which are basically a cloth version of a disposable, where everything is sewn together. The only downfall is that they take much longer to dry in the dryer/on a clothesline. You can get lots of brands of AIOs, but the most popular seem to be Fuzzibunz and Bum Genius. They range about $17.95 per diaper. It seems like a lot, but trust me, it's waaaaaaaaaaaay cheaper than spending the dough on disposables over the years.
Another is the "pocket diaper", which is a cover and a fleece inner with a pocket that you have to put an insert into. It's very nice because the fleece keeps the baby feeling dry, and it's easy because stuffing the pocket with the insert before putting it on the kid really isn't that bad. Pockets/inserts are much quicker to dry in the dryer/on the clothesline.
My hubby and I have been using Prorap covers and prefolds. We used to use Fuzzibunz overnight, but she grew out of that size and weren't able to afford to get her new ones, so we've just been double stuffing and putting an insert in her Prorap. Works really well.
For washing prefolds/covers:
When you originally get the diapers, wash them on hot water with 1t of ORIGINAL Dawn dishwashing soap to remove production chemicals. Rinse using cold water, TWICE. Then dry in the dryer. Dry them two or three times to get them super-fluffy and absorbent. The more they are dried the more the weave fluffs and thus the more absorbent it will be. Don't worry about drying the plastic/PUL covers, as the PUL reacts well to the heat.
For the Fuzzibunz and such, just follow the directions on the tag.
AFTER DIAPERS ARE SOILED: Do a cold rinse. You can do two cold rinses if they are especially gross. Drain all water/spin. Refill and soak for at least half an hour with OXICLEAN or a wannabe oxiclean. Drain again. Wash with hot water with half the recommended NON-DYE, NON-PERFUME detergent (if you use too much soap, the suds remain in the cloth and make it less absorbent, and if you use a detergent with chemicals/dyes/perfumes in it, it makes the diaper less absorbent). If you need to, just do a second rinse and that should be fine. DO NOT USE BLEACH. DO NOT USE FABRIC SOFTENER, either in the washer or the dryer - all chemicals make the cloth less absorbent, cause leaks/wicking, and make the diapers break down much faster.
[edit] If you have spots you want to get out, the best thing to do is to put them out in the sun, usually on a clothesline. The sun is a natural, non-chemical, and FREE ball of bleachy goodness! :D Also, if your diapers ever start repelling, or not absorbing well, just strip them again (use Dawn dishwashing soap instead of a non-dye, non-perfume detergent).[/edit]
HOPE THIS HELPS! :) Yay for cloth diapers!