I believe when you say 10 to 20 computers, you are thinking of hubs. Hubs share bandwidth. Switches separate collision domains so your design should work fine. Depending on how secure you want to make the network, you might also consider locking down each port on the switch by MAC address. This would prevent individuals from plugging devices into the network without your knowledge. You might also consider turning off file and print sharing and setting restrict anonymous to 1 to restrict the amount of information that individuals can pull from your computers.
Dig deeper on LANs (Local Area Networks)
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