Teemo's not really a support, most people play him as a on-hit/attack speed bruiser hybrid top lane, or as AP, and in lower levels and Elo, he ca be effective as AD. He can do a lot of sustained damage through building magical on-hit effects while being fairly tanky through items like Frozen Mallet, Madred's Bloodrazor, Malady, Wit's End, Sword of the Divine, and maybe even Guinsoo's rageblade. Keep in mind this is magical damage mostly, so what most people reccomend is putting masteries as 9/21/0, making sure to take magic penetration, while putting in 21 points in defense to be beefy enough to fight, being sure to take increased HP, regen, reduced damage, and all, especially because of his hidden passive, "global taunt." Take either flat armor pen, armor pen and attack speed, or armor pen and attack damage as runes, and either health per level, or armor yellows and magic resist or magic resist per level blues.
To build AP, the main source of damage is mostly from your shrooms and picking off people who unfortunately get by your ultimate, or fortifying yourself and your team during battles and skirmishes in fights. AP Teemo can easily take a person from 2k health to 0 if farmed enough from mistepping on 3 shrooms. It also affects your poisons and the nuke from your Q, so it's not bad as a unconventional burst/debuff mage. I still reccomend the same runes and masteries, but you can take magic pen and attack speed if you'd like.
As for AD Two phantom dancers and a Infinity edge, hextech gunblade, bloodthirster, all great items. This typically means building him as you would any AD carry. But this path isn't as survivable, and his range is too poor to be justified to play this way for the benefits, but you can build anyone like this actually and stomp anyone in lower levels. The fact that you were allowed to get this far in the game meant that the enemy was bad, or the game was way too long.
Teemo is a very versatile, strong, underestimated, extremely annoying, and a huge threat to the enemy when played correctly, but Teemo is also the most killed champion in the game, which might be saying something. He can be played top, middle, bottom, support, or even jungle, he has a variety of builds from debuff mage, to bruiser(best), AD, or just pick whatever you like. He can escape nearly any situation with move quick and ghost, and the map control, blind, debuff, large damage, and tankiness he can potentially provide to the team makes him definitely a very solid pick, just don't be a baddie noob feeder Teemo. I swear I see 20 for every 1 good Teemo I see.