I'd actually go the opposite way of the Blitzcrank guy and recommend taking a LESS specialized support, so that you can get practice with a few different mechanics at once.
Morgana's a good one: you have a line shot, a dot mechanic, an AE denial mechanic, and a countdown ult that you need to prioritize your items to use effectively. Plus, despite all that, she's easy enough to use that you'll probably to all right even before you're actually good with her. And if worse comes to worst you can use her to carry when all else fails.
If you really want to go specialist I'd also recommend Soraka over Blitz, you can damned near ignore the enemies and just focus on your team so it's the single easiest support in the game at the moment.
None of these are the "best" supports (including the ones other people recommend), but the actual best supports require an ADC that's either on the same page as you or in voice chat to pull off their really great combinations (e.g. Leona's infinite stun of doom) so it's best to get used to less friend-dependent ones first while training.