Good Synergy

Graves
Urgot
Corki

These are champions that are made to trade more often, which makes use of your healing to push the enemy out of lane.

Poor Synergy

Caitlyn
Jhin
Varus

These are squishy champions that don't spend a lot of time trading. You'll spend more time trying to poke the enemy lane than you will effectively using your kit.

Strong Against

Braum
Caitlyn
Thresh

These champions are either immobile or predictable in where they will be. As such you can avoid their attacks or harass them with your Q.

Weak Against

Blitzcrank
Zyra
Nautilus
Brand
Miss Fortune

These champions excel in punishing and zoning their enemies.

Health Regeneration is essential on Soraka due to her W costing her health, so taking as many runes to buff your health regeneration is tremendous.
Early game Soraka can have issues keeping her mana up while active in lane, by taking flat mana runes you're utilizing the effects of the Meditation mastery and it in fact provides you more mana regen than mana regen runes while at low mana.
There are no extremely effective marks to be taken as Soraka, Armor and MR are reduced on marks and you wouldn't get very much by dividing the 9 marks between the two so I take ability power to buff the rest of Soraka's kit.

In the Cunning tree
Wanderer is taken primarily for escapes, but can also be used for ganks. (though Soraka's ganks alone can be weak and leave her vulnerable between lanes)
Secret Stash or possibly Runic Affinity are choices here if you're going to have blue buff or epic buffs at any point.
Meditation is taken to increase your healing throughout the entire game and creates synergy with your flat mana runes.
Bandit or Dangerous Game are viable options here, I take bandit for the gold income but Dangerous Game can be used to increase your sustain if your team is doing well.
Intelligence is taken without question, it increases your HPS for the entire game.
Windspeaker's Blessing is taken to increase our healing and to buff our allies with our W, R, items or summoner heal.

In the Resolve Tree
Recovery is taken to further increase our HP5 which in turn means we can stay in lane longer or provide more healing over some time.
Explorer or Tough Skin are left to your choice, Explorer is better for ganking mid, but isn't terribly helpful for escapes. Tough Skin reduces the damage you take since you don't have very high resistances this is very important, but it can also be used to help you get your Bandit procs without worry.
Runic Armor should be taken to increase your HP5, your self-healing on Q and all healing recieved. Veteran Scars is not viable with this build and can in fact be disadvantageous since you do %max health damage to yourself fulfilling your roll.
Insight or Perseverance are both strong choices, the reduced cooldown on your flash and heal can be life saving but your perseverance will be essential in staying in lane where in other situations you'd otherwise have to recall or die.

At the start of your game you're usually going to take an Ancient Coin and Refillable Potion to start. Refillable potion is an extremely inexpensive choice that provides you with situational sustain until late into the game, its cost and use will enable you to get your items sooner.
Depending on how your lane is going your next item should either be Nomad's Medallion or Sightstone. While you're pushing the enemy turret, you should take Sightstone for improved vision, otherwise take Medallion. Don't forget to buy a pink ward when you're back.
You can also choose to take boots depending on how much gold you have and who the enemy lane is. The extra movement speed will help against skill shuts and AoEs and such.

After getting both Medallion and Sightstone you should rush Rod of Ages ASAP, it is critical to get this item early on because of how its stats increase over time. It can help your survivability to take Catalyst of Aeons before Blasting Wand since it helps with both health and mana.

Your Sightstone and Medallion can be combined into an Eye of the Oasis when you need an extra item slot, otherwise Boots of Lucidity or even a Kindlegem provide a greater buff that should prioritize.

Your next item will be Warmogs which will activate when you hit 10 stacks of Rod of Ages and Level 15 on Soraka. Warmogs will effectively completely negate the health cost of your heal while making you as a priority target harder for the enemy team to burst down thanks to all your extra health.

At this point, your 2 empty slots can be used situationally, if you want to use them for Armor or MR you can, but I personally take Ardent Censer and Mikael's Crucible to buff all healing done and to effectively negate grievous wounds.

Your first skill choice depends mostly on the enemy lane's comp.

Punishing champions (Annie,Brand,Morgana)
Mobile champions (Vayne,Ezreal,Kalista)
Take your heal first.

Melee champions (Braum,Leona,Alistar)
Take your Q first for harass.

If you take Spellthief's Edge, you must take your Q first as your Q will have to compensate for the lacking self-sustain Ancient Coin would have provided you.

Your heal should be maxed first, at a starting 8s cooldown, you will be lacking in effectiveness mid-game if you try to make your Q first instead.
Q should be maxed out second as it increases the effectiveness of your healing/harrass
E is generally leveled last, it's possible to put levels in this early to reduce the cooldown on it, thus making it more effective against a team with champions who frequently all-in.

Soraka's Equinox is also effective against champion traps like Caitlyn's E, Shaco's W and Teemo's R.

Summoner Heal should be taken with Soraka, with your keystone, it should provide additional healing and with Boots of Lucidity the cooldown will be reduced (even further if you choose to go with Insight instead of Perseverance).
Additionally, while Summoner Heal is unaffected by ability power, the power of summoner heal is increased by items like Mikael's Crucible, Ardent Censer and Forbidden Idol. Leading up to a maximum buff of +50% increased healing on your summoner spell.