Just my quick 2 cents…..I have been hosting at home since 1997. I have total control over my environment, have built many utilities that detect outage, and love the idea of hosting at home. It has worked very well for me.
HOWEVER (notice the caps), I would only recommend this if you are very technically inclined (I am a software guy by trade); otherwise, I would strongly recommend using a hosting company. There are way too many issues that you face hosting yourself, and if you are not equipped with the expertise to handle these situations, you can sink very fast.