* 赤ちゃん (akachan): This is the most common and general term for "baby." While it doesn't specifically mean *new* baby, it's often understood as such in the context of a recent birth announcement.
* 生まれたての赤ちゃん (umareta te no akachan): This literally means "newborn baby," and is a more precise way to say "new baby." 生まれたて (umareta te) means "newborn."
* 新しい赤ちゃん (atarashii akachan): This translates literally to "new baby." While grammatically correct, it sounds a bit less natural than the other options.
Therefore, 赤ちゃん (akachan) is the simplest and most commonly used, while 生まれたての赤ちゃん (umareta te no akachan) is more descriptive and emphasizes the newness.