The first thing to consider is the number of Ethernet cables that you propose to run. Whatever the number you decide upon, double it. The cable should be Cat5e, at a minimum, or Cat6. It should be solid core not stranded core cable. (Solid core cable for structured wiring, stranded core cable is for patch leads.) You should consider fitting a patch panel in the understairs cupboard and modular sockets throughout the rest of the house. Once all the structured wiring is in place, standard patch leads are used to connect the various items of equipment throughout the house to the modular sockets. In the understairs cupboard, standard patch leads are used to connect from the patch panel to the various networking items. A switch, a router, etc.
Switches can be unmanaged or managed; simple plug and play or complex devices.
For a router, the range is similar. With regards to an actual type, I wouldn't like to make a suggestion . . . as I have never needed to use a separate device. I am aware that Ubiquiti have a number of devices and have heard good things from people who use models from the "EdgeRouter" range. (if you really want to start spending money on a router, the starting point would be a Watchfront FireBrick FB2900, then Cisco and Juniper devices!)