You can use one of your current domains, just have to go change the mx record to point at the mail server... for example, all my adult domains are hosted on M3 but I do the mail for a couple of them here....
At your registrar, you should have access to where the ip for the domain is, etc.... The way I have mine set up is that I create a domain alias, such as mail.domain.com and point the ip to my home server, then I go to the email part and tell it that the email is handled by mail.domain.com....
On the IP, I have found in the past... That if I keep the connection live that I will not get a change of ip unless the line goes out.... But, I also found that if I went into my router and told it to always fetch the same ip, 99% of the time I would get connected on the ip I wanted... Sometimes though, if that ip was already assigned, I could not get it...
anyway.. any help I can give, let me know....
another alternative, at least for testing is to find someone with a mail server and ask them to set up for you for a while to see if that takes cares of the prob