I’m really no expert with wireless networks, BUT if there are 4 floors…. ideally you could have an access point on each floor and trunk them via wire to one switch which is therefore connected to the internet, all in the ground floor or basement.
Now, regarding access restrictions and remote admin, it depends on which access points you buy.
Most do have this capability. You can restrict access by only allowing certain MAC (physical) addresses on the wireless network. And as far as bandwidth utilization, this could be done through the switch or the access point.
Hope this helps a little.
Best of luck.