Congratulations!!
To answer your question about what you will need here, my advice is LAYERS. The weather is a bit unpredictable at that point, and your baby will start getting "wiggly", so she'll need some short sleeved onesies, some long sleeved shirts to wear over them that can easily be removed, a couple long pants, and at least one good sweater and hat. Just buy a couple things she can wear over those cute summer clothes.
As a mom, though, I would caution you against buying too much newborn/0-3 month clothing anyway until you know how big she'll be - if you have a 9 pound baby, my prayers are with you, and she'll never wear them anyway.
I've relocated once with a two week old, once VERY pregnant, and once with a 2 month old (we never did time our moves well) so if you need any advice, pm me!