Wifi Repeater from an Ethernet Port

Hi there

I am approaching finishing a basement development under my house, currently the wifi is very weak. What I have allowed for is an ethernet port from a cable that is connected to the exising modem router along with a wifi range extender in the hallway.

However I was thinking maybe a better option would be to have a second modem/router plugged into this ethernet port and use it as a repeater.

Would this work? And are there any recommendations for a good modem/router?

Thanks