Sometimes a lot of summoners just assume you can pick any support you want just as long as it's a support. They all do the same thing, right? They just support, right?
No. You're losing a big advantage if you mismatch your lane. Not saying you're going to lose your lane or the game because of it, but some supports just naturally work better
with different AD carries.
For Ashe: A natural lane choice would be Soraka. Why: Ashe has enough cc of her own to be fine without having any additional cc from a support. Her harass will essentially come
from using Volley and frost arrows. Upon reaching level 6 you're going to be firing her ultimate either in your lane or at other lanes. All these things require a lot of mana,
so picking Soraka here will help tremendously.
For Caitlyn: Cait is a great poker. She has situational cc, but in her case it isn't really required to do damage since she has such long range, so I'd go with Soraka in this
lane. Soraka can heal if she happens to get hit, and can also restore mana for her Piltover Peacemaker and ultimate.
For Corki: Natural choices would be Sona or Taric. Corki lacks cc but has very good damage, so having extra cc in lane like stuns/slows really make him powerful. You might also
consider Janna in some instances.
For Ezreal: He doesn't have much cc at all, but he's an okay chaser. That being said I think Soraka would be a good pick so he can keep his mana and health up. You could also
make a case for Sona.
For Kog'maw: Good at poking and he has a slow, so I'd pick Soraka. She just benefits poke champions the best.
For Miss Fortune: MF is a strong anti-healer with her impure shots and she works really well with Taric and also notable is Sona. If you can trap people under her E and R
it's going to inflict some real pain you can't easily heal from.
For Sivir: I'd just go with Soraka. Sivir is a great farmer/poker as long as she has mana, so Soraka would be a good choice here.
For Tristana: Tristana is really good burster for an AD carry, so she's going to work great with Sona and notable mention Taric. Sona would be the best choice. Tristana
also has an anti-heal in her kit and a displacement ultimate so she's great at securing kills.
For Vayne: Sona,Taric, and actually even Soraka all work reasonably well here. Vayne usually isn't going to have problems catching up to people so cc isn't an absolute
must in this lane, but having an aggressor like Taric and Sona also work great. Soraka works pretty well if you like using Tumble and Condemn a whole lot.
Note on Janna: You'll notice I don't mention Janna a lot. It's not because she is bad, but Janna is actually a pretty situational pick. If the other team has a
strong ganker like WW or Nocturne, or if bottom lane is surprisingly strong (like Tristana/Sona) Janna is going to be a good pick because she can blow people
away and ruin that surprise advantage. Janna does have some cc though, but she does lack lane sustain. That's her main issue.