I've seen the newborn size bumgenious and they are oh so cute!
Guess it depends on how skinny bub is as it may be too hard to get a good enough fit to contain poo and also the cost. They do heaps of growing and fattening up in the first 12 weeks so not sure if it would be as economical to use a lot of them.
Have a look at buyena as newborn sizes come up on there from time to time.