If you have good upload speed at home, you could do something like Apache.
There are also sites that offer free server (site hosting) that usually include access to a private fileserver (mainly where the site will be hosted from).
I'd say just upload it to one of them and do it that way to save time. Apache gives you 100% control though, although you'll need to set firewall rules on your router for redirects and blocking some traffic, which isn't terribly difficult, just time consuming.
I usually use 000webhost if I want to throw something up for others to look at, plus they give you a free subdomain to use on their site (or add your own if you purchased a domain).
It's a shame Dropbox killed their hosting folder (think it was called public), literally made this thing super easy.