Free and reliable hosting, from experience, tends to be mutually exclusive.
At 10Meg, running Apache as a webserver, you could do it at home. Pay the few bucks for a fixed IP or use
DynDNS...
At home the downside tends to be performance, your upload speed is limited. With low traffic, it isn't so much an issue. Also some ISPs block port 80, so you'd need a redirect
If reliability is a major issue, beyond that of assurances from the hoster, you need to get an SLA from them that has penalties. You won't obviously find cheap or free hosting with an SLA, but if you have to be sure....