I like Sivir for Ranged AD. Always nice to see that boomerang take off more than half a health bar of a few enemy team members during mid game.
Karthus is a decent AP champ although, he gets banned in draft sometimes due to his global ult.
I like starting off with the mana regen item plus some hp pots & maybe a ward. First time back, I usually make tear, hp pots, another ward, and boots @ 350 gold for more mobility if I have the gold. Second time back, I'll usually complete AP boots, + ward, + start on the hat. Note that if the fight is going bad early on/I am doing horrible against my enemy lane mate, I will buy more low level items in favor of completing the tear/boots for a more immediate boost in stats. Then later in the game, I'll finish those items out.
The rest of the time back is situational. I'll always buy ward(s). If the fight is going good, more AP items. If the fight is going bad I'm getting either a magic resist or armor item depending on who I'm fighting mid/how enemy team is built.
As for abilities, I save my first ability pick for what happens in jungle. If enemy invades jungle, I'll get 1st level of W to give my teammates time to flee or to position themselves to get a kill. If they do not invade, I'll get Q for harass in mid lane. level's 2/3, I'll get the other two abilities left from Q, W, E. Level 4+, I max q for more harass, then E for some fun farming, kiting, then W last. Train up ult whenever possible. Make sure to request your teammates ping/ask for your ult whenever they have a low health enemy.