I use the Bumgenius one size pocket diapers to great effect. They began fitting my newborn well at 9lbs (which was just 2 weeks in our case)as those newborn thighs are just too skinny! And my 3 yr old son wore them right before he potty learned at night. At just under $18 they are a good deal, IMO. Some larger Targets actually carry them now too which gives you a chance to try them without paying shipping.
I used BumGenius one size on my daughter when she was a new born. The only down side is that she was a longer thinner baby (7lbs, but 21 inches long) so her thighs weren’t very chunky. She also liked to sleep sort of on her side, so we had some leaking when she was on her side just because she was so tiny compared to the diaper. To fix this problem we used prefolds for the first month. Once her thighs fattened up after a few weeks it wasn’t a problem. Bigger babies should be fine.