Hire someone/a company who is skilled at low voltage wiring.
I could theoretically have done all of it myself, terminating the cables really isn’t that difficult. I got the equipment and set the equipment up. But I did not run the actual wires, and watching them do it. I know my strengths, they saved me days worth of work. And I wouldn’t have done as good or clean of a job. They should be able to help you with AP placement as well.
A good rule of thumb is, everything that can be hardwired is hard wired. If you think you will need more ports, add them now. If you need. 2 ports at a location, make it 4 or 5. Now is the time to do it. Run fiber to the locations that will require the opening of walls should you need to run more lines. If you are setting up an out door AP or location, run fiber to the exterior wall, connect it to a switch, then use the switch to connect it the device to the network.
I would go with a full unifi stack for the hardware, I think it’s the best bang for the buck hardware for this purpose. If you hire an A/V company, they may want to use Araknis, because of your home automation and Sonos, but I have no experience with it.
Make sure the network closet has adequate ventilation.
All your runs come to a patch panel. You want cat 6 or Cat6A depending on home size. pure Bare copper. If anyone recommends CCA, ignore them and find another contractor. A good UPS is a must.
I would run Cat6A not cat 5E. At least 5 runs to each room. I would run the largest reasonable gauge cable and have each rooms receiver in a closet along with the networking gear. I’d future proof running 2 fiber runs to each room.