Everyone here has given some great advice! Just a few things I learned while cloth-diapering my daughter...
1) I wouldn't start a newborn right away on cloth, the meconium doesn't come out of the diapers and managing care of a new baby while also doing laundry is just too much! I think it's a better idea to go a few weeks on disposables, and once you get your footing, move on to cloth.
2) If you use a diaper made of synthetic materials, you have to be EXTRA careful about what kind of soap you use to wash them in. It took some time, but my BumGenius pockets eventually got really stinky and started to cause a horrible diaper rash because I was using a detergent that (little did I realize) contained optical brighteners and (on occasion) scented oils, which built up on the fibers and were trapping urine residue. A lot depends on what kind of water you have, etc., but what solved that was using a really clean-rinsing detergent like Charlie's Soap (which you can order online, some shops carry it). Even the most earth-friendly detergents may cause problems.
3) The liners are probably best for after the baby starts eating solid food and the poop gets a bit more solid and sticky. Breastmilk poops are super easy to wash out and not a problem. I also have the ImseVimse "flushable" liners, but I NEVER flush them in my house because our plumbing is so old. I considered them more disposable if poopy, washable/reusable if just wet.
4) For little babies, I think the prefolds or contour diapers with separate covers are great -- you have to change them so frequently, that it's more economical and the diapers are easy to clean. But my husband is prefold-challenged, so he's more likely to use the pocket diapers (FuzziBunz, BumGenius). I'm looking into getting the new one-size FuzziBunz because they have easily replaceable leg elastic, which is a godsend -- half of my BumGenius dipes need all that elastic replaced after my daughter's use, and this is a sewing chore I'm not looking forward to.
5) My favorite diaper source is www.diaperware.com -- the owner (Inge) is outside of Philly and an AMAZING resource herself, happy to answer your emails and phone calls with advice to your questions. Fantastic customer service, and a super informative website as well. She also gave me a diaper care booklet produced by Bummis which goes into great, wonderful detail about how to care for your cloth diapers (of all kinds) and even lists about every single laundry detergent you can think of and whether it's good for cloth diapers or not. Ask her for it, she'll happily send it to you.
I hope all these answers aren't too overwhelming for you! But as a pp said, it's good to educate yourself beforehand, and also to try several different kinds of things so you know what works best. Congratulations on your new grandchild, and best of luck to your daughter!