Ap teemo is one of my favorite builds in the game, but it misses on lots of lil' hamsters potential simply because he cannot fight all that long, and if u get yourself into even slightly wrong position u'll just get instantly bursted down in no time, that's why we're only taking 20% of the AP build.
Rylai for some AP and load of additional HP, but most importantly for that oh so sweet satanistic slow from your Q.
Zhonyas for even more AP and armor, but this item is allways all about it's active, wchich is particulary useful on teemo, cause unlike most of the other champions you keep doing damage to your enemy even during zhonyas.

AD teemo is viable, and has always been viable, but he doesn't have nearly as much pure destroying power as AP teemo. Even though ad items on hamster are a bit worse scaling than AP they still somehow work, especially these with their active and passive bonuses which this build is all aobut.
Youmuus Ghostblade for a piece of AD, but it's active is whats drags us to it. Bonus movement speed from Youmuus + teemos W = infinite kiting potential.
Frozen mallet gives the same thing as rylai but with AD, and slow on autoattacs is important for your kiting as well because you cannot keep enemy slowed witch just your rylaied Q.
Mercurial Scimitar adds decent bonus to AD and M.Res which with armor from zhonyas and hp from ryali and mallet makes you super-tanky with addition of Scimitars active wchich helps your kiting even more, with all those items you are basically uncatchable.

What's interesting, and less known is the fact that full tank teemo i also semi-viable. Well, i day "semi" but it's more of situational build, if your team lacks a tank then teemo will do decent job with keeping enemies on himself because of his high priority, and can still keep up with constant DPS.
Items that give you tankiness where contained in the AP and AD chapters so not much to do but sumarise
You get ****load of HP from rylai and mallet
You get Load of armor and M.Res from zhonya and Scimitar

So we have 5 items, to that we add Boots of Swiftness and thats how we get the ultimate Hybrid Satan. As you have probably figured by now this build is focused entirely on surviving prelonged fights, but not by getting loads of life-steal or regen, but by beeing tanky and kiting extremale efficiently. With this build your opponent will allways be slowed, and you are rarely or never CC'ed, and that gives you the oportunity to go all-teemo on enemies faces.

Every needed information according to the masteries, runes, abilities etc.is in according descriptions.