Firstly you upgrade your starting item for extra gold gain and mana regen. After that you rush cdr. I usually prefer not buying cdr boots, and not upgrade boots until later, when I buy Boots of mobility.
Most often the best first cdr item is the Forbidden Idol because it's cheap and it helps counter the mana problems.
After you are close to the maximum cdr, you may consider upgrading the items you have bought. Upgrading the starting item is the cheapest and usually the best choice, except if you have enough gold to buy Ardent Censer.
Imo, Ardent Censer is one of the best items on Soraka, and sometimes it wouldn't be a bad idea to rush it even before completing the cdr. (Especially when you win your lane, and you have enough gold to buy it at once).
Zeke's Harbinger is also nice if your adc needs critical, and can also be rushed in such cases. Vayne, Ashe and may other adc's synergies well with it.
Spirit Visage is a quite expensive item, so it is not advised to rush it. The main advantage of Spirit Visage is that, while it provides hp (which sometimes harms Soraka), it also increases all regeneration/healing effects by 20%, which, in addition to the 150% regeneration, makes this item the best choice to provide Soraka with some hp with minimum harm. Only if the enemy is heavy AD this item isn't so worth.
Aegis of the Legion is another considerable situational item to increase your defense. It can be bought early if enemies in your lane have magic damage. While it provides hp, it's regeneration somewhat makes up for it. Locket of Iron Solaris provides too much hp and I'd advice against buying it, except if you have Ardent Censer and you desperately need some more defense. Banner of command is an expensive item, but it is the best choice to upgrade Aegis to. However, because of it's price, better leave it for later.
Mikael's Crucible is considerable if the enemy team has long stuns/snares like Morgana, or slows like Nasus. I usually consider this item if the enemy has at least 2 champions with long cc.
Choose an amount of items to complete your 45% cdr. You can't choose all.
Guardian Angel: After completing the basic build, especially if you have Spirit Visage and/or Aegis of the Legion, buying a Guardian Angel is a good choice since armor and magic resist synergies with the bonus hp, and it's passive is useful. Usually the game will end before you manage to buy it though.
Zhonya's Hourglass could be a usefull item, especially if you need some armor, but it's price is too steep and most of the time it's not worth buying, except if you are too fed.
Archangel's Staff isn't completely out of the question: It sure is expensive, but the shield can be used to protect you without burdening you with extra hp. It can also be charged quite fast with your Q. Finally, it provides a lot of ap which is very useful.
Frozen Heart can sometimes be useful versus a heavy ad team, or if your team needs a Frozen Heart (vs Vayne, Yi etc) and none of your team can afford to buy it. It provides 20% cdr and much armor, which would synergize well with Archangel's Staff not only because of the mana, but because the armor complements the shield. It could also be combined with Spirit Visage, but not very often because versus a heavy ad team you won't have to buy Spirit Visage.
Sightstone: it costs a lot for Soraka to get hp and occupy a space in the inventory. If you have to buy it, you better combine it with your starting item. If you do this, the best choice is to buy Eye of the Oasis for the hp regen. Otherwise you better skip buying sightstone
Warmog's Armor: At lengthy games, when you have Spirit Visage or something and you end up with more than 2.15k hp, this item can be very effective. Especially of you manage to combine it with some armor/magic resist (like Frozen Heart, Spirit Visage, Guardian Angel) it will make you a considerable tank. It's huge HP regen makes up for the bonus hp (provided that you end up with more than 3k hp). If you avoid taking damage, you can heal your teammates and regen the hp in seconds. However, it isn't worth to rush buying hp in order to buy Warmog's with 3k hp early in the game. The cdr and ap of other items is much more useful.