There is a problem with using your own SMTP server:
They are widely used for spamming. So, there is a public list of IPs and IP blocks used by ISPs for their customers. Even if you are on a fixed IP, that IP almost certainly comes out of the ISP's dynamic IP block (and they just config their DHCP server to always dish out the same IP to you).
These IP ranges are routinely blacklisted by ISPs.
So if you run your own SMTP server, you will find that a lot of your email never arrives... The situation is bad enough as it is, with so many people (and companies) running dumb filters like Mailwasher.
You can do it, but you have to set it up so that the email is stuffed into your ISP's SMTP server for onward transmission. That server is far less likely to get blacklisted, and if it does, the ISP will suddenly get loads of phone calls from irate customers and they will do something about it.
There is a very subtle config feature in sendmail to achieve this.
But even this doesn't work completely, because your own IP still appears in the email header...
There is a solution to all this hassle:
You set up a VPN, using Port 80 (HTTP). This is a bit tricky because Windoze doesn't do it natively; you have to buy a bit of software for the PC end. You then need to set up the terminating end, and this is usually a not-cheap VPN router. Most of the consumer VPN routers can do an SSH VPN. Then you set up an SMTP server of your own. Then you are sorted; this will work everywhere that provides HTTP (WWW) access. This is the ultimate corporate mobile solution. I've looked into doing it but can't be bothered to put in the time to set it up.
As regards having your own email address, it's no good relying on any ISP. ISPs come and go, they routinely trash their customer base so that everybody leaves, etc... You have to get yourself a domain name, and then you are sorted. The ISP becomes irrelevant. Domain names are so cheap these days..