I would advice that you use championselect.net if you need help determining in-lane counters, BUT you should not be playing a certain champion for the sake of "countering".
Pick a champion that matches your play style, play the easy and hard matchups with them. There is no point in counter picking if you are mechanically worse with the selected champion. You will need to understand the strengths and weaknesses of your champion versus particular matchups.
Picked Riven versus Teemo? He certainly gives close range bruisers a hard time. Evaluate how mechanicly good your opponent is witht hat champion, this should determine your level of aggression. Learn to tower farm and play it safe during harder matchups when your opponent is on par or superior than you. Realize that while Teemo would be troublesome to deal with in lane, during teamfights you have the upper edge with two forms of crowd control.
With that said here is a personal list of champions (I've played) which represent a particular playstyle and are relatively safe to play as.
Vladamir/Nidalee: Hit or miss champions, some people are instantly good with them others might take a while to get used to their more passive playstyle. Weak early game (Vlad is particularly weaker), will generally poke their opponents down while healing back the majority of the damage dealt to them.
Irelia/Shen: Weak laning phase, stronger mid/lategame. Irelia is a reliable initiator + anticarry while shen's ultimate allows him to consistently test the enemy teams mobility and ability to react to side push (which many fail miserably).
Renekton/Darius/Riven: Depending on the matchup these three can catch some players off-guard. Good damage and tower diving potential, can result in a very aggressive laning phase.
Cho'Gath: Safe laner, even when losing lane can still make a huge difference in teamfights with his feast and built in large health pool.
Malzahar: Easiest laner in the entire game. Very few mids can actually contest him 1 vs. 1, only problem is during teamfights Malz tends to have terrible positioning as a result of his ultimate.
Morganna: Safe farmer, junglers will have a hard time ganking her with her spell shield off cooldown.
LeBlanc/Veigar: Love to burst players down. Veigar scales better into lategame. Much harder to farm with than the last two, but that's alright these players love to farm champions instead.
Safe - Ezreal/Caitlin: Easy to learn and as safe as you can get for an ADC. Both get a jump and have an easier time zoning other ADCs. Although don't expect them to compete with a Kog'Maw or Vayne late game.
Aggressive - Draven/Sivir/Miss Fortune: Strong laners, with the right support can catch the enemy of guard. Miss Fortune has very good team synergi.
Lategame- Tristanna/Vayne/Kog'Maw: Hard laning phase. Pentakill late game.
Passive - Soraka/Alistar/Janna: Focus more on either peeling for their ADC or simply giving them the sustain they need to remain in lane. (Contrary to his skill set Alistar is not an aggressive support, inexperienced players will be shocked as to how fast he can die... Use him to disengage). Soraka is extremely easy to play if new to support, simpyl stay back, maintain bush control, and be a heal/mana bot.
Passive-Agresive?: Sona/Nami/Lulu: Good zoning potential, sustain, and bring some form of CC to complement their ADC.
Agressive: Leona/Thresh/Blitzcranck: Love to initiate, can catch players off guard. Sustain is not a counter to this play style. Success depends mostly on skill, a good Lulu can keep these three so low they will be afraid to initiate while a good Leona will punish the enemy duo when their CC or jumps are on cooldown.
Oh and one more champion...
Elise: My personal favorite, play her top, mid, jungle, or support. Love her mobility, CC, and burst potential.
That's just a suggestion of certain champions that embody a particular playstyle, find one you like. Take counters with a grain of salt.
You will end in matchups were your picks don't entirely counter theirs. That's fine! Build a Negatron to counter their fed AP Carry or a Randuins to slow down their AD Heavy team. Items are also another great way of 'countering' mathcups.
TLDR: Pick a champion that complements your playstyle. Learn the weaknesses of your opponents champions.