Time, money and all things in between. If you have time, and your site is not mission critical and you're just doing it to learn, then run your own server (if your ISP allows it - that or you're going to have to colocate somewhere).

I would NEVER EVER EVER consider running sites from home. EVER. Colocate if you want to own your own hardware.

Maybe you're asking when do you decide to go from shared hosting to dedicated server?

Unless you have the infrastructure and the technical knowledge (or the money to hire in a person with that knowledge) - then you want to stick with rented servers and a management team.