Basic home use kit such as that from Linksys or Netgear (and there are several other similar vendors) should be more than adequate for the network devices.
Buy a 12 or 24-port unmanaged switch as the central hub to which all your ethernet ports are "flood wired" back to, and connect this switch to your internet modem / router / firewall. Bear in mind that you can cascade switches downstream from the "core" switch if necessary, either permanently or temporarily.
You have choice with RJ45 cabling at the "data cabinet" end, assuming that you have cabled in ethernet wall sockets around the house, and the RJ45 cables gathered in the data cabinet - you can either terminate them with an RJ45 connector and plug them straight into the switch (being careful of the correct TX/RX wiring), or install a patch panel and then use fly leads to connect the patch port to a switch port. Given that you probably don't need the flexibility of the patch panel (your connections are pretty static), it's likely a no-brainer, although the patch panel can be more elegant, which could be a consideration of it's going to be visible.
I would strongly recommend that any wireless access points are hard-wired back to the central switch - I have had problems using a secondary WAP connected wirelessly to the primary WAP / router - the connection drops out too frequently.
3-4 WAPs seems a lot for a 3-bedroom house - is there a particular requirement (due to distance or construction material) for so many?
For the logical network side, I would consider using the internet modem / router just to do NAT / FW stuff and serve wired connections, not wifi, and use it to manage DHCP for the entire network, so that your other WAPs are all acting as repeaters on the same IP network, and do not serve DHCP. You can have each WAP with the same SSID or different - unless you have very widely dispersed APs, keeping the same SSID on all is probably best. Just ensure that they aren't all broadcasting on the same channel - use non-overlapping channels for adjacent WAPs.
There's some really useful information here that will help:
https://superuser.com/questions/1224...-access-points
HTH