Router in the main room. Switch from 1 port that goes to all the rooms. Each room have a 3 or 4 port switch, so if you need to have more than 1 thing plugged in you can
5e if you're cheap. 6 if you want to spend a little extra and get better speeds. You'll be happy you did it. Buy a spool of 6 and cut it to size. A lot more cost effective