Server 24/7 ?

Don't shut down your computer/server and use dyndns or something similar like this to avoid changes to your ip.
Other method would be to buy a server.

Yeah Teevision.eu is great to host a lagg free server for 2 hours but for more than one Teewolds-Srv a vserver is the best reason.

The IP would still change. DynDNS might help if you would share some low-priority data on the net where you can access via FQDN instead of IP (websites, vpn, ...) and where it does not matter if it's some time off while it switches the IP (you can't avoid switching your IP via DynDNS, you just get a  domain-name that is referencing to your new IP when DynDNS get's your new IP reported by some tool). A unique FQDN does not really help here.