I second www.no-ip.com. No-IP is an excellent service for this application. Ive been using them for over 8 years without any issues.

You may also want to take a look at a new product from Verizon which utilizes the 4G network for internet access. It provides an Ethernet port.

https://www.verizonwireless.com/b2c/splash/homefusion.jsp