If you are interested in using cloth diapers full time then most people recommend 24-36 diapers although I have gotten by with only 12 during some stages. Actually, I think 36 is too many. 12-24 is plenty. If you are using prefolds or fitted diapers then you will also need 4-6 covers. If you'll be using cloth wipes you'll probably also want 24-36 of those.
What kind of diapers you use depends on your personal preference. I recommend trying some of each to see what you like the best before you invest in a whole stash. A good way to start is to buy 24 prefolds, 4-6 covers, and a couple fitteds and/or pockets and/or all-in-ones. Then after you figure out what you like you can buy more.
A great resource for cloth diapering is www.diaperpin.com. You can read reviews of different diapers and diaper products and there is also a lot of info about cloth diapering and forums for asking questions.
My personal favorite for cloth diapering is fitted diapers with PUL covers when baby is awake and wool covers when he's sleeping. My husband and I both feel like fitted diapers are the easiest to use, and I prefer natural fibers to synthetic.
To be even more specific I like fitted diapers that have two rows of snaps. I prefer snaps over velcro because velcro can get ratty looking and you have to remember to fold the velcro closed before you wash it or it will snag other diapers in the wash. Also, I've heard that kids can undo velcro and take their diapers off, but snaps are harder for them to undo. I prefer two rows of snaps because I think you get a better fit. The top row is to adjust the fit at the waist and the bottom row is to adjust the fit around the legs. I have tried one-size fitted diapers (they adjust so you don't have to buy differnt sizes as the baby grows), but I don't recommend them. They don't seem to adjust enough to really be a one-size diaper and they don't fit as well as sized diapers.
I have two favorite fitted diapers. One is made of bamboo and one is organic cotton sherpa. The bamboo is trim yet absorbent and stays soft and flexible wash after wash. The organic cotton sherpa is also very absorbent and soft and durable. Sherpa refers to the finish of the fabric. I like sherpa better than fleece cotton because it looks nicer and seems to be more absorbent, but the absorbency could relate more to the brand of diaper. I don't know for sure.
I also use prefolds and pocket diapers when the fitteds are being washed or when I feel like a little variety.
You can get Chinese, Indian, bamboo, and hemp prefolds among others. Chinese and Indian prefolds are both cotton. I've tried both and at first I thought the Indian prefolds were softer, but after months of use and washing I can't tell much difference. Chinese and Indian prefolds come in bleached or unbleached. I prefer unbleached because it's more natural. I've also tried hemp prefolds and as far as I'm concerned if you're going to spend that much money for hemp or bamboo you should just get a more convenient diaper (i.e. a fitted). The real advantage of prefolds is their economy so if you start spending a lot on special fabrics they loose their advantage.
I've tried pockets with snaps and velcro and I've tried one-size diapers and sized. Although the velcro tends to get ratty and you have the laundry hassle I think you get a better fit and the diaper stays on better with velcro than with snaps. The one-size pocket diapers I've tried fit well at different sizes so I think they are better than the ones where you have to buy different sizes because you have to buy fewer.
Although I prefer snaps on a diaper, I think I prefer a PUL cover with velcro. It fits a little better than snaps. Since I've made all of my wool and fleece covers I can't say much about what I like best except that ones that wrap around are a little easier to use than ones that pull up.