Probably because I'm basic but I've always used healing and flash for my Soraka. This also is the best spells for her (in my opinion).
So why healing? Soraka always starts with very little health, so it can be used as an emergency boost for her. But I personally use it as a way to help the teammates in lane. It is a good boost for your teammate (whether it be that they needed the small amount of health to execute the enemy champion or to run away if needed).
So why flash? Because... its flash (you always need flash lol)

Okay, time to trigger people...
I have always used the general sorcery/domination rune that is given for free (yes, I know, I'm sorry). However, I do know for a fact that this is the better rune for Soraka.

....
Alright, let me explain:
When people see this, it can confuse a ton of people (maybe even tilt) on me. Why? Because who the fluff would build only health and mana but no AP! Well me, that's who. This build is why I'm known by my friends as the Soraka Ambulance. The health and health regen allow you (as a Soraka) to run into battle and heal your allies without killing yourself right away. I personally suggest getting Warmogs first, but that is just me. On top of that, you have cooldown reduction. You'll literally be able to get your abilities back in a snap, it's crazy.
Yes...it is insane! But I'm not a Mastery 7 Soraka for nothing!

This honestly depends on who you are playing with and against; not only that but what type of playstyle you are. I personally start with Q or E. This is because I play a more aggressive Soraka beginning game and try to push the enemy back. But if I'm playing with a more squishy ADC, I'll start with W.
Depending on how the game goes is how you'll know which abilities to level up.

Every time, I have fought these three... it has been a living nightmare to deal with. (I now automatically these three). I think it is because of the generally bulkiness of these champions and because.... the hook...