How do I make this script play music In order?

As you have a song id array you should use a numerical loop and not a generic for loop which can access in any order.

There are some other changes that you can make to help your code. First use event if there is one do not rely on things like wait() and second you are using script.Parent a lot so it is better to make a variable as you use the same ound instance each time you play a song.

To wait until the sound has finished playing you can use the event Ended and use the function :Wait() which will wait intil the event is fired and pass back any argument with the given event.

Example

local songs = {
    279207008,
    1610954983,
    1610958262,
    1610989227,
    1610995500,
    1611013339,
    1611019115,
    1611026677,
    1611030715,
    1611033388
}

-- make a variable of the sound since it is used multiple times and will not change
local soundObj = script.Parent
while true do
	for i=1, #songs do
		-- access the song id at the array index
		soundObj.SoundId = "rbxassetid://" .. tostring(songs[i])
		soundObj:Play()
		soundObj.Ended:Wait() -- wait for the song to finish playing
	end
end

I hope this helps.