I have been maintaining my companies exchange server for several years and have had to set up a couple of different exchange servers over the years as well. I have never gotten into web access though, but recently this feature has been requested.
Looking through the settings in exchange it seems as though things are set up. I can not seem to access OWA outside of the company though. I am assuming that I am missing something that is probably pretty basic. Internally I can connect to OWA by using http://ip.address/exchange
for example). We do not currently host our own website on this server but I am willing to purchase a domain and link it to this server if that is necessary.