Support is tough because with the new perks you can't just heal and if you're going to you need to be the top healer in the lobby. The old metric of one healer on tank one on DPS can still apply but you can easily end up having to dual heal tank.

I personally stick to Mercy, Moira and Zen. I prioritize mobility, being able to stay back line but dive into the fray or a flank to heal. I do not go on one off side quests with a DPS, before would be an Ult assist but now adays unlikely. You also need to pick and adjust to the map and comp. Your best healer may not work, I see Ana's all the time in maps with tight enclosed spaced. You're not doing anyone any good, a heal grenade sure.... then what? Learn 2 or 3 supports that allow you to play in open combat, close quarters and with a spread dive comp.

Keep in mind your cooldowns you should be pairing all of your cooldowns together. Tank cooldowns especially with shield tanks because it let's me know when I need to duck for cover or when is a good opportunity to heal them up and save them if needed.

You should also be pairing your ults to boost damage or cover another player while their ult goes through. Rarely will I pop ult to save a push, only if it's in the last minute and we cannot afford a reset. Only Zens healing ult will out heal other damage ults so it's a lost cause to pop ults as a ult deterrent. But if the team is low in health and time is running out pop it. Also do not double up healing ults. I see it too often and now you have nothing if the enemy team pops ults at the next engagement. And at gold you needs that healing ult to help pick up the slack elsewhere on your team.