Considering cat5e supports 10gbps up to almost 150feet, you have little reason to go beyond it. Strictly for the client to server communication cat5 would be perfectly suitable since 100mbps is way beyond anything you need for online gameplay. So basically whatever grade of cable that will max your internet bandwidth is what you need, unless you are doing something exotic in your internal network. Also I'm not actually recommending cat5 (good luck finding it anyways).
Edit; I'll add cat5 often supports 1gbps anyways.
Edit; I'll add cat5 often supports 1gbps anyways.
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