afaik serving websites from your home dir is a bit odd, since the user running nginx/apache shouldn't have access to it, something like /var/www is way more common.
and asuming you don't just use git for deployment but also for it's core purpose version control you should setup the origin to the actual origin and name the remote where you push to accordingly (production, dev, test, staging) and you shouldn't set it as the default push, to avoid excedently deploying when you just wanted to checkin the code to the origin repo!