PSA: Teemo's E does not proc Rylai's, buy Frozen Mallet
And if you're honestly buying Rylai so you can have a slow on your Q, why not buy Hextech GLP instead? AP, Slow and Health, but also gives you mana
Also Nashor's Tooth is good but much more efficient in a full AP build since the added auto-damage is increased by AP. Prioritize Runaan's/Wits End/Rage Blade if you're not going full AP "Q you for half your health" build!
(If you are, have fun)