Washable diapers can be washed at home or by diaper service. Disposables vary by brand: excellent Huggies, smelly Pampers, leaky Luvs, cheap store brands.
You will most likely use diapers for the first 2-3 years of your child's life. To use disposable or washable is up to you. The net result of the many arguments for either sort is that it doesn't make any difference. Every child learns how to use the toilet between age 1 and 3 on his own (on her own it's likely to happen earlier, actually).
I tried potty-timing with my first child starting at 3 month and failed. My next attempt with her was at 19 month, it took 2 month and it worked -- she knew how to use the toiled, was extremely proud of herself, and looked better in her underpants than in bulky diaper. However, she had accidents until she was 3. With my second and third I had other things to do and didn't bother with their potty-training until they were cooperative or gullible enough for me -- 2.5 years with the second, with the considerable preassure from the older sister and three weeks struggle, and at 2 and 8 month with the third -- he learned how to use the toilet in two days and never had accidents.
Disposable diapers are waterproof and sanitary, they are obviously easier to use. Some people claim washable diapers are more environmentally conscious, but some studies suggest that production and lifelong washing and drying of washable diapers is more energy- and resource consuming then production of disposables. Disposable diapers are clean by definition, but one may doubt the chemicals they put inside the thing (which is a quite harmless polyacrylic gel which will clog up you washer nicely) and dislike the papery texture. I never bothered with washing.
Disposable diaper is made of paper and filled with absorbing gel. It is kept on its place with wings which stick to diaper itself. Cheap brands have pieces of adhesive that sticks to the skin as well, more expensive ones use a velcro-type closure. Inside of the diaper there are several layers of soft absorbent paper that pulls the moisture away from the baby (it stays dry to the touch with a cup of water in it). Outside is glued through and almost waterproof, but actually lets some air in and out. Don't worry about "almost": the liquid inside is locked in the gel. Some brands claim to have aloe vera somewhere in the diaper. Some diapers are scented. Yuck.
Very small baby will soil up to 10 diapers a day, and you have to change the diaper every time, so it seems to make sense to buy cheaper brands. However, cheaper diapers are more likely to leak (and you will spend on washing) and/or cause allergic rush. I liked unscented Huggies best. Sizes for the disposable diapers are given in age and pounds. Pounds are more accurate. Usually the same package size of diapers cost the same for the same brand -- whether it's 72 diapers of 1st size or 58 of 4th. The older the baby, the less often you will change the diaper. One newborn-size Huggies diaper will hold up to 1 1/2 cup of water (barely). I actually tried. There are usually products of the same brand -- "superabsorbent", "overnight" and such. They usually vary in thickness and proportion. There are also swimming diapers and training pants on the market. Swimming diapers are thin and are not "breathing", they are unsuitable for every day wear. Training pants are thinner than diapers and usually have some small patterns which disappear if the thing is wet. The idea is that the toddler will try to keep the stars and flowers and be proud of himself if he managed that.
See also: children, newborn baby.