Hello, my summonername on NA is TheInconspicuous and I am a 1900 ELO player who truly loves Teemo. Though I have never taken him into ranked play, he is my favorite champion and I play him frequently in normals whenever I need to carry my friends. Here is my specific build to Teemo that I have heavily tested and tailored to my playstyle.

GP10 Quints: I run these because they are simply put, the best runes mathematically for any character. Gold = Items = Kills = Gold, very easy investments.

Gold let's you build powerful items - Phreak

Attack Speed Marks and Seals: Attack More for easier farm, more damage, more harass, dominate lane, and farm at tower effectively.

Critical Chance Glyphs: Critical hits in lane turn the tides in Teemo's favor. Basic harass turns into shoving your opponent out of lane.

30-0-0

Go full offense to dominate lane because you scale off of both AD and AP.

Doran's Blade: Doran's is great for dominating lane as Teemo

Mobility Boots: These give Teemo great map control along with the mobility to contest and force global objectives. Perfect to carry your teammates by winning their lanes for them.

Avarice Blade: More Gold More Crit, perfect for Teemo.

Soulstealer + Sword of the Occult + Levaithan: Because Teemo is a perfect character to win lane and kill your opponent early, you need to snowball your advantage. Teemo has great AP and AD scaling, so Soulstealer and SotO are perfect items. Levaithan is great for not getting focused down. All of these items are very cost effective.

Executioner's Calling: This item was built for Teemo, it gives Critical Chance, Lifesteal, and another healing debuff on top of your ignite. This item is also cost effective when compared to other AD items, much like Sword of the Occult.

Trinity Force: Tons of Damage - Phreak