the 1st teemo is the most rounded one and is my favorite in this build,my original build.

its good at 3x3 and 5x5 either

the 2nd teemo is a powerhouse of Attack-Damage and Critical-Strike and isnt for new-teemo-users.

its better in 5x5 matches cause it need more gold to be done

the 3rd teemo is the Ability-Power one and the powerhouse of mushrooms,put it all over the map for ambushing,teleports,kills,assists,running and chasing deadly.

good at 3x3 cause of the little time to say GG before the second needlessly large rod

the 4th teemo is a great jungler when it reaches lvl 7(everyone thinks that junglers are guys who just keep jungling and dont play the game but teemo isnt nice in anything until getting some itens like the 2 first reccomended ones(of my list)
the trick is to only go kill monsters with you powerfull shroom when you get Rod of Ages and end with Blinding Dart.

this teemo is good at 5x5 and 3x3 matches either

the 5th teemo have a high critical hit chance and a high critical hit damage(5 criticals=almost death)and dont need to be a good chaser cause of its awesome damage.

this teemo is better at 5x5

-AS Teemo

Pros

-Very Nice To Ambush
-Best Chaser
-Getting Fed Early = Victory
-Powerful Mushrooms
-AWESOME SPEED

Cons

-if you Dont Have Boots at Lvl 10 You Have a High Chance of Defeat
-Cant do anything Without Mana
-NEVER do 5x5

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-AD Teemo

Pros
-More That 1000 Damage With Critical at Lvl 18 with ALL ITENS
-Very Well Rounded
-Monster at 1x1

Cons
-Bad Chaser
-Not For Noobs(sorry)
-Cant Be Effectively if Not Fed Early Game
-ONLY FOR PROS(sorry again)

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-AP Teemo

Pros
-Good at Team Battles
-Good to Chasing
-Double Armor Debuff

Cons
-Cant do 1x2
-Low Armor
-Cant do Anything in Turret Dives

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-Jungler Teemo

Pros

-Nice at Killing Champions Minions and Monsters
-Get Buffs Quick
-Good at Farming Creeps
-High Attack Speed

Cons

-Bad Chaser
-Bad at Early Game
-Bad Jungler Until Get Madred Razors

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-Assasin Teemo

Pros

-Ultra High Critical Damage/Critical Chance/Attack Speed
-Good at Team Battles
-Assasin
-Sure Godlike When Got the Second Phantom Dancer
-Good Even at Disvantage Like 1x2 and 1x3
-Can Mid Easily
-Have More Pros That All Teemos of This Guide

Cons

-Low Health
-Bad Chaser