I recommend trying on of the sampler packages. This will give you an idea of the options and which ones you like. Or, buy a couple of kinds off of one of the used sites, like www.myuseddiapers.com or
www.diaperswappers.com.
The least expensive by far is prefolds with covers. The most expensive is AIO (all-in-ones, meaning the absorbent part and the cover are sewn together and look pretty much like a disposable, except fastened with velcro or snaps).
We use a combo of various kinds of cloth diapers. For me, I use primarily the prefolds (they are my fav) and covers. I like the prefolds best because they are frugal, they wash great, are absorbent, and I like the fact that I can get a custom fit by the way I fold and/or pin them (if you don't like the idea of pins, try a Snappi--it's sort of like the thing with teeth that you use to hold an Ace bandage on, but safe for the baby).
DH uses fitted diapers with a cover, or AIOs. DH likes the simplicity of the fitted/AIO, and I hazard a guess to say, he really likes the AIOs best. They are really like using a disposable, in terms of ease of putting on/taking off, and anyone can easily & quickly learn to use them.
If you want to cut the costs of cloth diapers, buy used (see above links), check Freecyle, and/or sew or make friends with someone who can sew--sewing fitted diapers is really pretty easy (I can say this, and have sewn several and am a beginning sewer).
We also highly recommend using flushable diaper liners, especially for the newborn phase. My brother & his wife, very "eco" people, tried cloth dipes 2x (once with each child) and were "defeated" by the poop issue. It just grossed them out too much to have to scrape or hose poop into the toilet. With the flushable liners, you just drop the liner & poop into the toilet & flush, so there's minimal contact.
Depending on how "eco"/"frugal" you want to go, you can also get reusable diaper wipes of flannel or terry--you wipe, and drop the used wipe in w/ the diapers and wash them all together. I wanted to do this, but DH was too grossed out by this, so we use disposable wipes. But he's doing cloth diapers, so I'm not gonna complain!! :)
I do use the cloth diapers when we go out around town. I use gallon ziploc bags with a little bit of baking soda (to help absorb smells) to hold the used diapers and just put them in the diaper pail when I get home; I can fit about 3 used diapers in one gallon bag. You can't carry as many cloth dipes in the diaper bag, though, as you can disposables, and they are bulkier and weigh more, so that part I don't like. For trips longer than 1 hour in the car, or overnight out of town for the weekend, we tend to use disposables unless we know for sure we have time to do the laundry before going home (I just can't stand the thought of hauling a load of dirty diapers in the car home after a vacation).