Ubuntu Server needs to inform me of a new IP address when it changes
I am running an Ubuntu gaming server on my home network, behind a router and firewall. My ISP is Verizon, and my external IP address changes from day to day, rarely going a week the same. This makes it difficult for other people to access my server consistently, and requires me to get a complaint, go home, check my IP, and then tell them all. Verizon doesn't think I pay enough to have a static IP, and I agree.
How can I get Ubuntu to check what the external IP is, and then forward that information in the form of a text or email if the results have changed? I have rudimentary Ubuntu skills, and my reaction was to write a script checking the IP and then sending the updated address to an (e)mailing list of recipients. I would then have cron run the script every ten minutes or so.
1: Is that idea feasible?
2: Would someone help me write that script if so?
3: What is a better idea?