I'm setting up a new network and looking for some hardware recommendations for switches, access point (and router?) Realistically looking at a total network hardware spend in the order of $500
The network topology will look something like this (the coloured boxes show groups of computers that share data)
Switch #1: Needs PoE to supply other switches. Would it need to be a managed switch?
Switch #2 & #3: unmanaged and powered from PoE
In terms of the general network configuration:
The network topology will look something like this (the coloured boxes show groups of computers that share data)

Switch #1: Needs PoE to supply other switches. Would it need to be a managed switch?
Switch #2 & #3: unmanaged and powered from PoE
In terms of the general network configuration:
Will VLANs be useful?
Prefer to use DHCP for IP addresses, which piece of hardware (a router?) would assign them? Is any extra hardware needed?
The access point would be great to have 2 SSID, one directs public accessible wifi to the local web server (probably Abyss) (question: is it DNSmasq and port forwarding to achieve this?). The second SSID connects into the rest of the network. Would they be on different subnets?
Any recommendations for providing an internet connection to one of the servers? It would probably be from a usb 3G modem. Simplest would be to plug it directly into the laptop...