I main Heimerdinger. So obviously, I would tell you to get Heimerdinger (heavy bias). Here is why.
He has excellent lane presence because of his turrets, and he wrecks any melee carries early to mid game. FIghting close to enemies is beneficial to him since it is easier to land his grenade and rockets tend to aim better. That being said, he is the squishiest champion in the game. (I start with Ruby Crystal as my first item for the health. Then turn it into Rod of Ages)
His turrets are downright terrifying early game. He can put out a lot of damage with a single turret level 1, provided the enemy is stupid/your jungler can stun him in range. His rockets may seem a little weak, but with enough AP they shred mid game since most people don't build too much Mres. His grenade is great if YOU CAN LAND IT. If you can't, there goes your combo of stunning people near your turrets.
Item suggestions: Rod of Ages for health and mana (he has INSANE mana costs early game)
Ionians (Personal choice, I like frequent turrets and I get Void Staff anyways)
If you want, Rylai's
A lot of peeps use Liandra's Torment, but it isn't that good on Heim. If his turrets procced it like Singed Q did, but it only works on rockets and grenade (as far as I know)
tl;dr Heimerdinger is amazing against close range enemies, takes significant skill to play as he is UP at the moment. Recommend.