How to access the PlayerGui via script and this happens?

1st Box: When I have this script run I get this message " ServerScriptService.Script:2: attempt to index field 'PlayerGui' (a nil value)". Also how to access the PlayerGui with scripts? I am unsure of what this means and how to do this. I have tried rerouting it to StarterGUI and it works (I'm asking about this so I can learn).

1st Box

game.Players.PlayerAdded:Connect(function(player)
	wait(1)
    game.Players.player.Name.PlayerGui.EnterGui.TextLabel.Text = " " ..player.Name.. " has joined the game"    
    wait(5)
    script.Parent.PlayerGui.EnterGUI.TextLabel.Text = " "
end)
--This is my code for Players

2nd Box: It does work for StarterGui but that brings me to my next problem. I want it to remove the message after a wait, as shown in the Second box of code below, and that doesn't work as well. No error code appears and I am unsure as to what is wrong. Can you help with this. Thanks!

2nd Box

game.Players.PlayerAdded:Connect(function(player)
	wait(1)
	game.StarterGui.EnterGui.TextLabel.Text = " " ..player.Name.. "has joined the game"
	wait(5)
	game.StarterGui.EnterGUI.TextLabel.Text = " "
end)
--This is my code for StarterGui

When using PlayerAdded, the player parameter takes the instance of the player already, so if you do game.Players.player, the script looks for someone named "player" in Players. What you want to do is actaully player.PlayerGui or game.Players:WaitForChild(player.Name), both of which work fine.

Secondly, you don't want to mess around with StarterGui too much, since that just changes the template that is applied to everyone when they either reset or first join the game. If you want to change the message, be sure to access PlayerGui instead of StarterGui, which applies to that specific player real-time.