I like Heimer top, can't say much for mid. Pros, you have good siege, harass, and, if you land your E, a nice bit of CC. You can dish out a surprising amount of damage at level 6, with your empowered rockets. Not only that, Heimer is pretty fun to play, as you can focus more on dueling, as your turrets help with csing. Cons, you have pretty clear boundaries, as you lose a lot of damage when your not near one of your turrets. Your E is moderately hard to land, and is a bit strange to use. Until you get a Rylai's, you don't have much chase potential, and that can be pretty frustrating. Masteries, I go either go 12-18-0, with thunderlords for poke, 18-12-0, with DFT as the keystone. In a lane you feel your going to lose, you can go 0-18-12, getting thunderlords and regen masteries, to help out in lane, due to your absurdly high base regen.
Anivia, I don't play, so I'm no help here.
Karthus, personally one of my favorite champions, is a good pick, if your prepared to spend time getting good. His theme is cool, and you can deal a significant amount of damage, while being pretty tanky. Pros, you have good waveclear, a nice ult, and your passive guarantees you will be able to deal some decent damage, even if you get caught and killed in a teamfight. Cons. you have no hard CC, your Qs are pretty easy to miss/have dodged, and your ult can be pretty easily countered. If you get caught as Karthus, its unlikely you'll get away. Most people prefer to go thunderlords on Karthus, as its pretty easy to Q, AA, Q, however, I prefer DFT, as it allows for a nice burn on your ult, more damage on your Qs, and helps with your overall power, as Karthus's AP ratios are pretty garbage.
or any spell shield or skill that makes you invincible/untargetable (morgana shield, sivir spell shield, vlad sanguine pool, etc) hard counter karthus's ult.
ahri