If you're happy with the performance of your Belkin router then you can plug it into the new Modem/Router's LAN port and continue to connect through it. Locate it wherever you want. One problem though, computers connected to the different routers will be in different Subnets (IP address ranges) and therefore unable to communicate for "File & Printer Sharing", if that is a requirement.
What is Amazon Go and will it come to the UK? The store without checkouts or queues