Couple of thoughts (caveat: I'm not a cable installer but have done CCNA so have some idea of the issues).
One thing - only one spare port on the second switch, may want more for flexibility/future-proofing.
Also to be detailed would need to know distances between switches (different rooms?) and the max bandwidth requirement of each device.
Cost is always a factor and cat6 may be 20% more or so than 5e, so may not be cost-effective to wire every device cat 6 (assuming none need the speed) but would definitely consider cat 6 for the interconnects between switches and router. Again future proofing to consider but unless your devices need 1Gb connections 5e should cover the device links.
Thought on the topology - if you lose the top 16 port switch you lose all connectivity, might be better to have all 4 switches individually connected to the router in a star topology via a switch at the router itself (according to BT site the hub 5 has 4 ethernet ports anyway so switch is built in, but one may be for the outside connection). That way if you lose any switch only the devices connected to that switch go down (VOIP phones if POE go completely dead!).
May be a QoS consideration too, you've got voice data, video data and computer data running over the same links, VOIP phones don't like packet drops and video similar, may want to consider VLANs for each to get more control (again would depend on spec).