Must learn Kassadin because of his awesomeness
counters: AD carries

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.

Malzahar is an underrated boss and i consider him a must know.

I would say
Anivia:Amazing wave clear long range aoe stun wall that gives vision nuke that scares the **** out of carrys.Durable due to passive. Wall gives vision and set up well can change a game.
Ryze: tanky endgame and does rediculous damage as well. His early game can be fixed with runes. One of the few champs that can 1v5...sorta.
Orianna: Great for protect the carry utility comps..I don't play a great deal of her but know I appreciate it when I'm the tank or adc.
Karthus: Ulti is an easy way to get fed amazing wave clear, wall with mr armor shred slow and giving vision...(why isn't his w nerfed?) q spam for days e does damage almost as high as a fiddle ult. passive makes you god mode with infinite mana for 7 seconds.
Leblanc: the go to shutdown the enemy carry, rediculous burst can transistion to a cc mage as needed.Highly mobile
Twisted fate: great wave clear shoves down towers long range q nice burst when setup right. Ult gives vision of all enemies on map in addition to allowing you teleport within a large range.
Ahri: High mobility, long range single target cc aoe damage on low cd that does true damage. Spell vamp passive...kites for days with rylais
Morgana: Can't stop her farming or pushing your tower, Passive spellvamp, ult that burns flashes and or wins the fight. Considered a support by riot but otheres dissagree due to the massive coefficent on her q.( what was it like .9?)
Swain: level 6 your the little engine that could if you get chalice and blue buff. Good aoe cc high sustain great damage with combo, amplifies true damage from ignite. If worried about ignite just get cleanse.
Gragas: your go to anti initiation mid. Highly mobile tanky with w pokes like a boss..r just don't mess that one up.
Vladmir: you hit overdrive at 9 when you do no ones really going to be able to stop you because of great damage high sustain and natural tankiness. Wave clears rediculously fast.
Hope this helped. As mentioned above you don't own just because you play the champ thats flavor of the month more often you'll win because of knowledge experience and knowing how to plant your skillshots.

What the dude above me said, I would suggest Ahri and Cassiopeia.

Ahri is just a common and really good pick and Cassiopeia has one of the safest laning phases in the game.

Cassiopeia is my favourite champ, because her damage potential is endless. Due to fact that she can spam her E, she can put out almost as much damage as the AD carry late game.

The new champ Zyra is also a good choice, she has a fairly easy laning phase and has lots of utility.

Don't forget the two old school mages, Annie and Vieger

I learned 3 champions well and you can pretty much counter anyone with them.. annie because shes so easy to farm with no matter what and her ultimate and stuns are late game changers. Leblanc because once you figure out how shes really suppposed to be played there are only 3 people you should lose to-- Galio, Fizz, and if they're really good Vladimir but they increased sigil speed so hes pretty easy most of the time. People say shes not good late game but if you do your job correctly it will most likely either be a 20 minute surrender or their mid will be useless whole game. AP Yi- made fun of a lot, however if played and built correctly can be a serious problem. This one I only pick if other team has low cc/silences but if they are lacking in that area its pretty hard to die with him and you can outfarm anyone. Good luck.