Unless you're on a static IP (most ISPs charge extra for that), then using a plain old domain name will mean downtime every time your IP changes (for you to realize it stopped working, then updating it, and changes to propagate). For those type of scenarios, there's really only 1 solution: DynDNS's custom DNS service (perhaps others have a similar service, I never actually looked). Your DynDNS client app will make it update the IP "instantly" (just like for any usual DynDNS entry), with no downtime. Namecheap.com supports dynamic IP updating and offers a wide variety of top-level domain registrations.