Cable splitters

I have a splitter within my outside box with one line for my modem, one for a TV in the kitchen, one for a TV in the basement and one to our attic which is then connected to an amplifier/splitter for X1 service to our other TVs. I purchsed a smart TV for the basement and was wondering if I could split that signal at the wall to a modem for wired internet connection to the TV, and a second for our Legacy HD box that we are using now. This would avoid using WiFi for the smart TV functions. If so, do I need an amplifier too? I was planning to buy the modem and splitter on my own and not rent  from Comcast. Any suggestions would be greatly appreciated including best products to purchase.