Newborn babies go through about 8-12 diapers a day. That means that as a new parent, diapers are a big part of your life. You don't need leaks slowing you down, you need reliable diapers for your baby.
Huggies Supreme diapers come in sizes newborn to toddler. I've never had a problem with leaking with these diapers. The outside feels more cloth like and moisture is wicked away from your baby's skin allowing them to feel more dry. Newborn size does have a cut out for the umbilical cord.
This disposable diaper is a popular one. Though, unlike it's Supreme counterpart, it does not come in newborn size. The first size available is a 1. No leaking or other problems associated with this diaper.
Pampers hass a variety of different diapers for each stage from newborwn Swaddlers to toddler Cruisers. These are designed to help prevent leaking. While I've never had a leaking issue with these diapers, the newborn variety seem to had an odd smell to them. Despite that these are very popular diapers.
If cloth diapering is up your alley, I highly recommend the Kissaluvs fitted diapers. The snaps make finding the right size for your baby easy and the newborn sizes come with top snap downs to protect baby's sensitive umbilical cord area. These are not all-in-one diapers (AIO), you must use them with covers to make them water proof. These diapers are also cute, particularly the colored diapers.
The Kissaluvs Contour diaper give you a bit more bang for you buck by allowing the diapers to not be fitted. These cloth diapers simply sit inside your cover. Can be used with or without doublers.
The Bummis Super Whisper Wrap is an easy to use cover for any cloth diaper. You simply attach to the front of the pant using Velcro attachments to tighten and loosen as needed. You can use a wrap for multiple diapers, so you will not need as many wraps. It is important to remember to close the Velcro closures prior to washing.