How to give my Minecraft server a custom/dedicated IP?

While the IP address will be based on WHERE you have it set up (so if you set it up at your own place, it would have the same IP address as you)… HOWEVER, setting up a Domain Name for it makes it a bit easier for everybody to access without having to officially disclose your IP address.

For Free DNS services, http://freedns.afraid.org & http://www.noip.com are currently the best options available… With FreeDNS as the recommended option as it has the most flexibility for the least amount of cost (being $0.00 / yr). FreeDNS also allows you to utilize your own domain name, should you choose to spend money to register for one (~$20 / yr for general domain names… More for specialty names… MOST registrars usually have a promotional rate for new domains with standard prices for renewals).

Hope this helps!