in the distant past, I ran a tiny http server on some throw away hardware for hosting files on.
that was before ISPs decided that DIY server hosting was "bad, m'kay", and before the rise of serious ddos and hacking groups. I eventually pulled it down when I found google had metcrawled it despite my robots.txt, and absurd abuse of all the signs and flags meant to say "DO NOT INDEX ME!!!" to metacrawlers, and found my host being added to pirate sites. that gave me waaaay too much unwanted traffic, and was horrible the number of portscans and hack attempts I was getting per hour.
Google does not know the meaning of the words "private" and "no" when it comes to indexing content. thier crawler explicitly ignores about 2 DOZEN ways to advertise that you do not want to be indexed, and indexes anyway.
I would still be incined to host a small httpd (really, your home router already does it, it just does not expose it to the internet. A little reconfig, and it can host a few image files for simple sites like this one off of USB just fine) if I could keep it from getting indexed by the likes of google, and then having every chinese hacker on the net trying to pwn my server.
in light of that, the use of a cloud service, like a small webhost, is a wise choice.