This is a pretty broad question. Are you trying to set up a local area network? wide area network?
For the local area network, you are most likely going to set up a fast ethernet network with at least 1GB interfaces for the computers and gaming server. 10GB ports are making their way to enterprise networks. Whether 1GB is enough is going to depend on how much bandwidth you really need. 1GB interfaces may already be enough.
For the wide area network, again its going to depend. What you need to determine is how much bandwidth is going to come into and out of your network. You need to determine the upload and download requirements.
If it's a gaming center, most LAN games are designed to run on very little bandwidth to support internet play.
Any modern center should have at least gig to the desktop. Alot depends on the specifics. Will you host servers, multiple types of games, will you provide internet access to desktops as well. Will it be a BYOD style center? Do you have a startup budget?