There are many free providers on the net that have been more or less stable for many many years. I'd believe that free is the cheapest you can get.
As for reliable, I wouldn't go with an unlimited or free host but rather one that states precisely how much resources you can use with your account.
Nothing in the world is unlimited. For example, many providers that offer unlimited space will shut down your hosting account or warn with you a limited number of warnings if you attempt to store more than one backup or store personal files outside of web related space. If you never intend to store large files or use your account to move large files then this shouldn't be an issue, tho I've seen many customers complain about this storage issue in my career with other companies.
In the end it is up to you, You can pay for an unmanaged service and no help and get cheap unreliable servers where your site may go down sometimes, or you can pay a little more and hopefully get a more reliable service with better assistance from the company.