Wiring

I had a AT & T installer out today for internet 50. He wanted to run the wire on the outside of my house which I did not want. Also would not make the run to my TV where I wanted the Wi/Fi router. I am willing to run my own wire. Should I run cat 5e or cat 6? I was going to terminate wire with a rj45 jack behind the TV. The other end goes to the NID? Thanks for your time.