I tend to start with the 180 mana/5 and the 180 hp/5 and wards so I pretty much always get a philo on my first b + w/e gold I have left. If I only have 350 more, I'll get boots. If I have 700 more, I might get a sightstone or still just get boots and also pink wards if I feel the need. If I have 1050, I'll probably go ahead and get boots and sightstone.
I wouldn't get aegis on most supports. The upgrade is too expensive for most supports unless it's a really long game. It should be built on your jungler or top laner. There's no exact order anymore. You can go for an early philo if you think the lane will be easy and your ward coverage will be fine. You can rush a sightstone. You can get an early kage's. The kage's upgrades are fantastic and I love getting them. I delay getting shurelya's sometimes.
for Lulu mana isn't a problem for me a all even without mana regen runes, and I max Q>W>E..
So I build Sightstone, Philo, Kage, Tier 2 Boots. From there I get a Kage upgrade, I LOVE Twin Shadows, Ruby Sightstone and Shurelya. That's 4 items right there so the last two I usually go Iron Locket and the Crucible.
Taric I go Emblem of Valor > Sightstone > Philo > Aegis
You should probably tell us what supports you play. As other people have said, it kinda depends on who you are. Like Aegis works well on tanky supports, like Leona, while it doesn't work as well on squishies like Zyra.
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Build 1 can work on anyone, makes you tanky. You will have a lot of HP, armor, MR. People with innate tankyness like Taric, Ali, and Leona will love this. Taric especially with the built in armor buff. Even if someone else gets an Aegis/Bulwark, the aura stacks on either person, plus it is nice for laning phase and/or small skirmishes. Zekes is good for AD heavy teams.
Build 2 is good because of Mikaels. I recommend this as a healer build, such as Sona and Soraka, even an alternate build for Taric. With Mikaels you will be able to spam abilities, so I love it on Sona. Literally just faceroll QWE all battle. The heal/cleanse is also nice. The shard isn't bad, use it on yourself or someone else for the AOE slow. You can use it to block the enemy from attacking your ADC.
Both have locket and shurelyas for the stats and actives. Ruby sightstone is obvious.