Perhaps just go with how you're feeling after the birth. When you ring/sms people to tell them be sure to say if and when you're up for visitors or you let them know when is a good time.

DS was born at 4:42 in the morning. We rang our parents and immediate family around 8am and told them visiting hours were after 4pm. They weren't really, we just said that so we could have the day to ourselves quietly. Then after our immediate family visited we sms'd everyone else. I found that most people asked when a good time was to come visit so I was able to reply on a case by case basis