It depends, I like to choose a support based on the ADC early game play, if the ADC is squishy, let's say for example Ezreal, I'm more likely to pick Soraka or Sona to sustain him on lane. But, if you have a more sustainable ADC, you can pick a more aggressive support like Leona, Nunu or Zyra.
Another thing to observe is the synergy of Support/ADC level, Leona has her Q,W and E ready by level 3, which can combo really good with Graves, where in this level he's really great. We could also mention some good combos like Ashe and Janna, due to the synergy of Janna's Shield and Ashe's crit, and Ashe's slow with Janna's slow.
Besides, picking a champion that you enjoy playing, which will also help in your performance, you could ask the ADC which support he enjoys to play with, if he has any preference and you feel his preference is useful, you could pick it too.
I found the League Support Suggester, a recommendation software to provide the best support for your current needs.
I've also found the following chart which really helps me when to choose a good support for my ADC, I usually pick one of the three recommended:
Your in-game score is irrelevant for LP gain/loss. It is calculated based on the game's estimation of the relative skill differences between your team and their team, as calculated by win/loss history; and by the difference between your current LP and the game's estimation of your skill level. This second category helps dampen the effects of streakiness, and ensures that there's a penalty for a loss even in D5 of a league.
As a side note, if you have that many kills as Shen, and your team keeps dying, it's possible that you need to work on your teamwork a bit more, saving people with a well-timed taunt/shield.
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The "honors" you see in your profile are the number of times you've been honored, not the amount of honor you have. Each time you're honored, you gain a quantity of honor depending on who honored you. If someone rarely hands out honor, its "worth" more than someone who honors each and every time he plays a game. There is no way to know your exact honor value, they keep that number secret on purpose.
As stated in the Honor System FAQ, honor can decay over time, and this may cause your Crests (ribbons) to disappear. Crests are not permanent by design, you have to constantly keep playing and receive honor from your fellow players to keep a Crest.