How long do modem routers last

If taken care of and configured well, seems like they last a while. 

You can take the modem/router to your new place and connect it up. If your using the same ISP. If the ISP is different, contact them first to see if they support what you have been using. 

If you feel the modem/router don't work well at the new place, you have a couple of options. 

1. Bridge the modem/router and use it as a modem. Then connect a external router to the modem for better wifi and router handling abilities. Any WiFi router will work in this configuration.

2. Use the modem in router mode, disable the modems wifi radios and connet up a wireless router in AP mode. Used the wifi router in AP for your new wifi operation. Youl could connect a NG Orbi wifi MESH system in AP mode for great coverage if you have a larger home. Or any other standard non MESH wifi router will or in AP mode as well.