We waited until about a week, when meconium was gone etc.
We used BBH petite small to start with and they were great - our others were all too big (sized and multi-fit ones). Some were too big around the legs, some around the waist. It depends so much though on the specific baby and the nappies. As our daughter has grown (3 months) different types have worked at different times as she changes in size and shape.