I accidentally clicked the back button on my mouse after typing up most of a great comment for you. So I am extremely sad.
Basically, you as an individual want to pick depending on your position in the pick order. Don't pick anyone who can be hard-countered easily if you're first or second. 400k Mastery on Ryze means nothing against even a 50k Mastery Sion. If you're closer to the end of pick order, check what the enemy team has and what your team needs. Often, it comes down to whether or not you need to make absolutely sure your team has at least some targeted hard CC, because the champions who can easily dodge other forms of CC are the most difficult to deal with. Luckily, this is possible in every role.
For example:
Enemy team has:
Your team has:
and you're last pick Support.
You can see that they have three champions who are very susceptible to hard CC. And your team already has a Sion and a Jax.
But neither of them have targeted hard CC, which is a problem since Yi and Kat are incredibly mobile and will be able to dodge both Sion and Jax.
You don't want a healer, since their entire team has enough damage to render even a Taric's healing useless. And you don't want an artillery mage support, since they'll easily get to you if you pick Brand, and they don't have the CC to make Morgana's black shield useful.
You could risk them dodging your stuff too, and go with Leona or Braum. You definitely don't want Thresh against Yi since your lantern can give him an extra dash if he hitches a ride on an ally.
But your best choices would be supports with relatively high damage for a support, and hard CC that is either instant or targeted.
That means you want
,
, or
. Since they all have targeted hard CC and can supplement damage to make up for Sion's relatively low damage. (Lulu can build Ardent)