You would need either a DHCP server, or to setup static IPs on the machine. Static IPs would probably be better so that you know which client which server will be talking to. You will need to use a different IP for the servers as the .0 IP address can’t be assigned to a computer. You can use .20 or something. You don’t need a layer 3 swhich, you need a layer 2 switch as you don’t need to do any routing.
You could setup VLANs if you wanted to, but that isn’t needed. Just plug in all the machines, assign the IP addresses and fire up the software.
Network switches don’t come with DHCP servers, so if you decided to go the DHCP route you would need a machine to provide DHCP, or have one of the servers handle it. In this case I would go with static IPs.
You can look at this: https://learningnetwork.cisco.com/thread/2253
But, to have smaller pools of IPs for each set of ports, you need some VLAN capabilities, and then you would need to enable routing between them.
I am still not clear on that. From what I can understand, I think I would need to create a VLAN for each Target Client. However, how where would the DHCP assignments have to bet setup?