OK, just to make sure i understood everything correct:
You want to set up an Mailserver on your private Computer. This computer sits behind an router. You want to send and recieve E-Mails with this server. Right?
Then you need to do this steps:
Set up an account at your preferred DynamicDNS-Service (dyndns.org for example). If you have an fix IP from your ISP and a registered Domain this step is not necessary. In both cases you need to set the MX-Record to your IP, if you use DynamicDNS-Service you will find an option in their Webinterface you can activate.
Forward Port 25 from your Router to your Server. Open up Port 25 in your Server Firewall if you have one.
Now you have to configure your Mailserver. He needs to know the domain he have to collect mails for. Just work with the Documentation of hMailserver: http://www.hmailserver.com/documentatio ... figuration
Your Domain Name in the Domains & Accounts Part and the Public host name would be the same.
To configure the other stuff, i need to install the hMailServer here, that will take a while. I will continue when I've done this.
PS: Most Mailservers do not provide an Webmail Interface. The only Server i know is Microsofts Exchange Server. But setting up an Webmail script is very simple.