Teemo isn't a very good champion (on Summoner's Rift), but if you're going to play him you should play him AP. Every ranged DPS champion is better than AD Teemo; there is no reason to build Teemo for AD when you can just pick one of them.
The only niche he has is his mushrooms. There is literally no reason to play Teemo other than his mushrooms. They provide excellent map control and ganking potential, and if your team knows what it's doing even provides potential in team fights, and - GASP - actually facilitates juking, which is otherwise barely existent in this game.
Deathfire's Grasp is completely key to AP Teemo and should be your first item. It is a very solid nuke, and combined with a beefed up blinding dart + toxic shot allows you to wear down a large chunk of HP from just about any champion; Teemo doesn't have enormous burst, but he has enough to be a great harasser, which the rest of his skillset facilitates perfectly. He isn't cooldown dependent, unlike most nukers; he doesn't lose a big chunk of damage when his ult is off cooldown. Unfortunately, this also means he generally doesn't have a big chunk of damage that other champions do have. This is why you need DFG.
Sorcerer's Shoes and (situationally) can also be key; Mushrooms have a .8 ratio, which isn't bad per se, but considering their base damage you normally get more damage from reducing enemy magic resistance than you do from increasing your AP. Void Staff is also a necessity if the enemy team wises up and starts to get some MR.
And then we come to Rylai's Crystal Scepter, because the only thing more annoying than 60% slowing mushrooms is 75% slowing mushrooms and 30% slowing blinding darts.
So your core items are Deathfire's Grasp, Rylai's Crystal Scepter and either Haunting Guise or Void Staff depending on if the enemy team is smart enough to get any MR outside of Merc Treads (which hasn't gimped mushroom damage in a while, by the way; some people seem to think it still does. it now only reduces the slow duration, not the damage itself). After this it all becomes situational:
Enemy team relatively squishy and loves hitting mushrooms for some reason? Zhonya's Ring is your friend here. What I said about AP ratios earlier still holds true, but Zhonya's gives such an enormous AP boost that it will make any nuke scary.
Team lacking in sustained DPS? Can't quite clean up surviving enemies after your initial burst in teamfights? Enemy team excessive on tanks? Madred's Bloodrazor is here to save the day. Yes, this is predominantly an AP build, but Bloodrazor deals magic damage - it will benefit from all that magic penetration you have, synergizes with your poison to a degree, and Teemo's attack speed is naturally quite high. Hell, maybe you'll even get some good use out of your passive with it.
Brilliance elixirs are important to have almost all game if you don't have CDR runes. Teemo loves CDR, but he's slightly difficult to itemize for it. You should be masteried for 9% CDR (6% utility 3% offense), which means 24% with DFG, 34% with brilliance elixir and DFG, which is close enough to 40%. More mushrooms = more frustration for the enemy.
I'm sure there are other good items out there, but honestly my Teemo games rarely last longer than Rylai's. The core items are all you need on Teemo. And please for the love of god avoid AD Teemo.
Oh, and one other thing; Teemo is pretty much a support. He makes the enemy team afraid to go into their own jungle, cuts their escape routes and gank routes and just generally pisses the enemy team off. His team fight presence isn't spectacular, so you have to make sure every blind counts; I know it's tempting to nuke that squishy Annie, but trust me your team benefits more from 3 seconds of Yi not hurting them. And I can't stress this enough; ALWAYS PLANT MUSHROOMS. If your ult isn't on cooldown you're doing something wrong. There are so many great mushroom spots that are 5 seconds from your lane that there's really no excuse not to plant mushrooms there. Hell, if you really have every possible space covered, just stick one at the edge of your lane; you never know when some poor sap might try to gank you and that single mushroom can turn it into a kill on your side.