I couldn't find these names on Google, luckily voogru gave me the ones for TF2, and after some tinkering I figured out the ones for DoD:S too. Just tried the ones that I thought would work on CS:S, and they did. So for anyone who needs it, these commands show the class selection screen to a player in TF2, DoD:S and CS:S.
Code:
ShowVGUIPanel(client, GetClientTeam(client) == 3 ? "class_blue" : "class_red");
ShowVGUIPanel(client, GetClientTeam(client) == 3 ? "class_ger" : "class_us");
ShowVGUIPanel(client, GetClientTeam(client) == 3 ? "class_ct" : "class_ter");
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