Running in-wall in a finished house can be a pain. Never know what's inside the wall. You can run through the floors and "along" the walls easier, but it's ugly. Either way, don't crimp the ends, use "punch-down blocks" and/or wall "biscuits" so you have female RJ45 on both ends. Also leave a "service loop". And if we are gonna run 1 cable, we run 2 just in case. Cat 6 minimum these days.

Might be easier to move the cable modem / wireless access points to the middle floor for better coverage..