It really depends on what kind of mid laner tou want, if you like to burst down your lane enemy from the start go for LeBlanc (note that LeBlanc is an assassin NOT an ap carry, she has very low team fight potential since her burst works single target)
If you want to harras your enemy from safety take Lux, Cassiopeia or Viktor, they have good range in theirs abilities and thei can do a lot of damage on team fights (these kind of champs need good positioning in order to be effective)
If you want someone that has good sustain and can be long periods of time in the lane try Swain, Kennen, Akali or Ahri. Swain can be long in the lane since he will restore mana through his passive and after 6 he can heal himself, Akali and Kennen use energy so they can stay as long as they have HP to stay (Buy spellvamp for them its critical that they have it), Ahri as long as she has mana she can heal through her passive.
For counter it really depends on the skill you have with x champ vs the skill of x champ that the opponent is using, safe picks are morgana or Lux that the first have amazing push power and teamfight potential or have superior range and can harrass from long range the second.
Passive farmers that have weak early game (Veigar or Ryze) can be countered by aggressive play early game or mages with strong early game (LeBlanc), when its the opposite champs with sustain or that can harras better these aggresive mages can shut them down early and in easy manner.
But the ultimate counterpick its the experience, trying diferent champs for different opponents will let you know how to handle them and how to play against them. Playing champs will let you know how the move and what tricks can do.
for example, I play LeBlanc a lot and the way I handle her when I have to face her is by denying her farm and kills, harras when you know you have better range, and pushing her away from the minions will let you win the lane.