Cert from Start SSL not trusted

Cert from Start SSL not trusted

On a small non-commercial website I am using a no-cost Class 1 cert from
Start SSL. There is no sensitive data going over the wire, but I do feel
that I would like to provide at least a minimum of privacy to whoever
browses to the site. When visiting the site in Firefox one receives the
"Untrusted cert" warning. Here is an example using wget:
$ wget https://example.com/images/dog.jpg
--2013-08-09 15:21:10-- https://example.com/images/dog.jpg
Resolving example.com (example.com)... 54.43.17.16
Connecting to example.com (example.com)|54.43.17.16|:443... connected.
ERROR: The certificate of `example.com' is not trusted.
ERROR: The certificate of `example.com' hasn't got a known issuer.
The FAQ entry from StartSSL states that to avoid the warning, one must
install the intermediate CA certificate to the browser. It is a bit
unreasonable to expect all website visitors to do that!
I don't mind installing a cert from a larger company, but while
researching the situation I find that the larger companies have the same
issue. Another fine ServerFault question mentions that the server admin
should install an intermediate certificate, but I am not sure that an
intermediate certificate exists for Start SSL. Before moving to another
company, how would I know if they have all the proper intermediate
certificates that we would need? As the previous two linked questions
demonstrate, even going with Verisign or GoDaddy may not resolve the
issue.
This is a conventional LAMP stack (Ubuntu Server 12.04, Apache 2.2)
running on Amazon Web Services.