This isn't an issue if your server is hosted on a dedicated machine or a VPS.
Things to consider:
Before using No-IP's service, you should know if you're on static or dynamic IP. If static then there is no need for you to use such service(s).
Hamachi is only usable when you're unable to do port forwarding and/or unable to configure, or you're having difficulties doing the procedures on port forward part
Go for dedicated server(s) or VPS when going public, you only host your server at home/office/school for testing purposes.
Note: There are actually cheap VPS service(s). I myself go for these to host my test server(s).
@Topic
When you want to release your server to the public and still play on the same machine, then the proper IP Configuration would be:
LAN IP
WAN IP/no-ip or any DNS service(s)