Family visiting in hospital

FTM and obviously both sides of family are very excited. I am getting induced in about a week so we already know what days I’ll be in the hospital. I have decided that the first day after baby is here will be just me and my fiancé. But that the second day I am more than happy to have family come visit. The thing is my family isn’t as big as his so I thought have my family come in the morning and his in the afternoon would work best just so there’s not a bunch of people there all at once especially because I know the hospital will only allow so many people in the room at once. My fiancé thinks we should just have people show up when they show up, but I’m worried that everyone will come all at once and then it’ll be a bit overwhelming for not just me but also baby. How have other parents done having family come up to meet the baby?