It really depends on your baby. We started using Target brand with DS when as soon as he was in a size 1. I didn't not care for the larger sizes of the Pampers and Huggies brands and I saved a lot of money.
Now DD is 7 weeks old and we had only used Pampers Swaddlers until last week when I ran out. I bought a pack of Huggies Snug and Dry. I used 7 and we had 7 blow outs. Also, they feel like tissue paper. We switched to Target brand with her too and love them.
After all that, I guess I'm no help. I don't know how they would be on a newborn. We started with size 1 with both kids. I like the cottony feel of Pampers swaddlers in the newborn size. I bought a large box off of Amazon before DD was born. It ended up being 13 cents a diaper and free shipping, Maybe check that out if you don't want to pay so much.