I really want to answer your question but it's so hard to answer. It's one of those things that's way too situational for me to be able to explain.
If your team needs a tank then you can go tank Naut, Leona, and Alistar are all fine choices and bring a lot to their teams. It's really personally preference. I would also like to throw Braum and thresh in there as well. Although higher skill capped (harder to pick up and do well with without much practice) they are still really good at what they do. Braum is really good vs a lot of projectiles, such as jinx, ez, ashe to name a few. Thresh is overall a good champion because his lantern is very unique. Again those two are much hard to master but with practice are really good champions.
If your team doesn't need a tank (At least one tank, I like to go a tank even if we have 1 tank, but NEVER if we have 2.) Instead I go someone who brings more damage to the table. I suggest (if you want to try and put your destiny in your own hands) picking up damage supports such as Annie, Brand, and Vel'koz. Using a support with damage allows you to carry yourself. I REALLY recommend Brand support, he's super fun and easy to pick up.
You can also go a less damage more support orientated champion like Soraka (I suggest as well, really easy and good) Sona is really good right now, Janna is really good and easy to pickup, Nami, Zyra (her damage is insane as well),
TL;DR
The point I'm really trying to make is that all these champions can do well and although you may need to synergize as far as going tank or not after that's decided, you really could pick just about any support champion and fit into your team. I more focus on what the enemy picks which is hard to tell you exactly what I would do without being in that position with the exact circumstance.
Examples: The other day I picked Tahm Kench because the other team had veigar (which happened to be support, didn't know it at the time) so I could save someone who got stunned by him because it was going to happen no matter what. I pick Morgana into Blitzcrank 95% of the time because she's going to make it impossible for him to do his job if you're good enough with her. I picked Naut into Kalista because his hook is really wide (generally wider than Kalista passive takes her) which meant I would have an easy time locking her down.
Honorable mentions:
Blitzcrank (really good at low elo because people can't dodge)
Morgana (My personal favorite and first main support champion)
Tahm Kench (Not the greatest right now but he is still useful)
Karma (She's really good but kinda complicated with using her ult right)
Lulu (She's not in a great position right now but she is still useful, She has a higher skill cap though)
PS: Feel free to look at my match history at the champion choices I've made based on my team and/or their team. It's almost entirely support games with some other games mixed in here or there.
