IMHO-I would go with 3 months so it can be used a bit longer. They grow out of newborn sizes so quickly.
Susie

Well, there was a 19 pound baby last week but that's not average. I think average is 7 or 8 pounds. Mine were 6lbs 3 oz, 7lbs 11 oz, 7lbs 3 oz, and 6 lbs 11oz. I had a friend with 9 pound twins, that's big!

Ok, I just read your question again and I realized I answered incorrectly. I should just go to bed and call it a day.
Susieq2u is right 0-3 month size last longer than newborn. But you usually need a couple of things that are actually newborn size to get through the first couple of weeks.

Carters NB size is 5-8 lbs, up to 21.5 inch, and 3 mos. is 8-12.5 lbs, 21.5 to 24 in. Most babies outgrow NB after wearing once or twice, but I can't resist buying those itsy bitsy things. Macy's had them on sale 65% off, and an additional 10% off if you use Macy's card, so they were giving them away!

OOPS ladies ,I am sorry! I will reword my question: What's the average size embroidery for new born babies? TIA ;D