That's completely dependent on how many shrines you do and what you get from them. In the run I'm currently doing, I did Vah Ruta with three hearts. There's no measure of how many hearts you "should" have at any given moment, since it's entirely up to you where you go and what you get out of it. You don't have to do Ruta first, either. BotW is a game where you make your own steps. You aren't lacking anything.
Do you think it would help me to better understand the spirit of Zelda to start with the older, original games? I know they are available on the shop.