Hi Ashley,
Yes, it is possible to set up a web server (e.g. Apache), PHP, MySQL and an email server/MTA at home, on either Linux or Windows, and run ListMailPRO there on a domain or subdomain pointed to your (preferably static) IP.
Often, though, internet service providers block outgoing connections to port 25, which is what most or all servers use to receive incoming email. Your ISP may also have a policy about running web or other servers which you should check into. You may need a business plan which could cost more.
An alternative I normally recommend is a dedicated server, such as available from
1&1 for as low as ~$60/mo, that allows you to host as many web sites and send as much email as you want. A VPS may be a less expensive option, but they are somewhat limited and may suffer performance issues, depending on the provider and other users on the same server.
Regards