If you want to do it right, try to get a static IP (you may need to get a business account). If your provider doesn't provide IPv6 to static IPs, go to some place like Hurricane Electric and get a free IPv6 range pointed to your IPv4 static address.
Alternatively, you might do a search for any DDNS services that provide IPv6 (I'm not sure if any do?), then that service will fllow your residential address when it changes. Either way I think you'll have some additional costs you need to weigh against your current hosting provider.