I'm still learning, but trying to adjust to New Soraka is even harder than I thought it would be. I first tried what I thought was pretty standard: Heal first, then Starcall, then that Silence thing. Well, that tends to not work out, because she becomes absurdly fragile, and Starcall has very little range and is exceptionally difficult to actually hit, as well as easy to notice and dodge.
During the laning phase, I find myself aiming Starcall behind them, as they're likely to simply run backward to avoid it. But because the casting range is so short, this almost always forces her to immediately retreat after casting it.
Realizing that Heal doesn't particularly scale that well and Starcall was just too slow to land, I tried doing the exact opposite: Silence -> Starcall -> Heal (Still of course getting heal at level 1). The Silence move is actually quite good for harassment. Its AoE is decent enough and it's instant damage. It also makes for an excellent escape tactic, as you can cast it in the path of your pursuer to halt them for a couple of seconds, which can make enough of a difference, as well as buy you time in case someone's coming to help. Combine that with a quick Starcall cast, and Soraka gets some of her health back, too, as well as a little extra bonus damage.
Again, I'm still figuring it out, but the way I used to do it--prioritizing Heal, Starcall, Silence, in that order--just doesn't work very well. The range of Heal, as well as the impossibility of casting it on herself, makes her exceptionally vulnerable. She can be quite helpful in team-fights and Wish is always an excellent move if your jungler runs into their jungler and things don't look good. But the Silence circle seems to be underrated right now. If nothing else, it scares the others on the bottom lane, and has proven helpful for both escapes and teamfights. It also scales nicely.
The way Heal works now is strange to work with, and Starcall isn't really doable for her to regain health, as it only works on Champions, not minions or monsters. But she can harass a bit better with the Silence circle, and if it detonates with an enemy Champion in it, it's an easy Starcall hit. You can only aim behind enemy champions for so long before they get the picture and just move to the side--the AoE is pretty tight.
Those are my personal thoughts on it.