How would I make a player's avatar change upon team selection?

There are multiple ways to do this. For the purpose of this, I will explain one way, and you can try to discover the rest based on this.

Note: This way will require an additional 2 random NBC accounts that the players will look like

First, let us set up our variables we will be using

-- Teams
teamCiv = game.Teams["Team Name for Civilian"]
teamSol = game.Teams["Soldier Team"]

-- Player IDs
CivID = "The Civilian dressed users ID here"
SoldierID = "The Soldier dressed users ID here"

Now that we have that, let's create a function for each team, to change the Player's CharacterAppearance

function changeCiv(player)
player.CharacterAppearance = "http://www.roblox.com/Asset/CharacterFetch.ashx?userId=" ..CivID
end

function changeSol(player)
player.CharacterAppearance = "http://www.roblox.com/Asset/CharacterFetch.ashx?userId=" ..SoldierID
end

Now that we have our functions, we can move on and figure our when we need to fire. We can do this first connect a PlayerAdded and a Changed event.

game.Players.PlayerAdded:connect(function (newPlayer)
newPlayer.Changed:connect(function ()
if newPlayer.TeamColor == teamCiv.TeamColor then
changeCiv(newPlayer)
elseif newPlayer.TeamColor == teamSol.TeamColor then
changeSol(newPlayer)
end
end)
end)

Now let's put this all together:

-- Teams
teamCiv = game.Teams["Team Name for Civilian"]
teamSol = game.Teams["Soldier Team"]

-- Player IDs
CivID = "The Civilian dressed users ID here"
SoldierID = "The Soldier dressed users ID here"

function changeCiv(player)
player.CharacterAppearance = "http://www.roblox.com/Asset/CharacterFetch.ashx?userId=" ..CivID
end

function changeSol(player)
player.CharacterAppearance = "http://www.roblox.com/Asset/CharacterFetch.ashx?userId=" ..SoldierID
end

game.Players.PlayerAdded:connect(function (newPlayer)
newPlayer.Changed:connect(function ()
if newPlayer.TeamColor == teamCiv.TeamColor then
changeCiv(newPlayer)
elseif newPlayer.TeamColor == teamSol.TeamColor then
changeSol(newPlayer)
end
end)
end)

NOTE: This is by far very inefficient, but it is the easiest way for me to explain to you a possible route. I recommend doing some more research and trying to do it yourself. Furthermore, this script was free written with no testing, so I apologize for mistakes that are bound to be here.

Sources:

http://wiki.roblox.com/index.php?title=Player

http://wiki.roblox.com/index.php?title=API:Class/Player/CharacterAppearance

(Assuming the team selection is using textbuttons) Make your script so when a player clicks the textbutton, then they would be changed depending on what team they chose.

I do not know the location of where you keep your clothes, so fill them in yourself on the first few lines. (BTW, this is for both teams, so just duplicate the script and configure them, and put them in the textbuttons.

ShirtID = PutShirtID
PantsID = PutPantsID

script.Parent.MouseButton1Click:connect(function() 
Shirt = Instance.new("Shirt")
Pants = Instance.new("Pants")
Shirt.Parent = script.Parent.Parent.Parent.Parent.Character -- Button must be directly under GUI. Not under a frame, or anything else.
Pants.Parent = script.Parent.Parent.Parent.Parent.Character

Shirt.ShirtTemplate = "http://www.roblox.com/asset/?id="..ShirtID
Pants.PantsTemplate = "http://www.roblox.com/asset/?id="..PantsID
end)

Please accept answer if it worked!