You'll definitely need a computer for every player; unfortunately there's no feasible way to run multiple instances of GE:S on a single computer, and this is mostly out of our control.
As for networking, you just need enough switches with ports to support every player, with the different switches connected to one other switch so that they all can communicate, with one of the switches connected to a router if you want an Internet connection (or just use the router as the central switch). In theory, plain 100Mb switches should work fine for GE:S. If you don't plan on having an Internet connection for whatever reason, make sure the server is started with -insecure to disable VAC.
You'll also probably want to have 2+ servers capped to 16 players or less. GE:S simply will not play well with 32 players in a single server.