I don't tend to buy much items. Do you?

I get: Sightstone, Ionian/Mobility boots, Shurelya's, the rest I dump into sight and vision wards. According to the stats I get about 7.5k gold on average as support.

Is this the common train of thought, or am I doing it wrong?

I generally play Lulu/Sona. My build usually ends up as

Sightstone, extra wards, Boots, Eleisa's miracle (from philo once teamfights really start going), Athene's unholy grail then Runic Bulwark. If it's late game I get a Warmog in Eleisa's empty spot and if it's really late game I'll replace sightstone with something like Twin Shadows

My core build, common for most suports, usually is:

Flask/2Sight - Philo/Sightstone - Boots - Aegis+Bulwark/Boots2.

I might get Eleisa's Miracle if I have of money, but wasting 1100 gold on merely extra sustain is very iffy. Particularly because I usually will end up getting Shurelya's Reverie sometime and therefore rebuild the philosopher's stone, and because I usually take exhaust rather than heal as a support.

But yes, Bulwark rush all the way. The item that really starts to help your team out, and also helps make your support more tanky so you need not die every single teamfight - since supports are generally squishy.

Shurelya rushing is also a common build I tend to see, but I don't encourage nor do I follow it often myself. That extra ms, while providing a lot of potential utility, does not have as much a large impact on teamfights to justify its early build.

I average 300 more gold than the games junglers

Shurelyas, locket and sightstone/pinks are the most important items you can buy.

Bulwark isn't a support item. It's a jungler/top item.
Never forget this.
It gimps your build terribly as a support.
Supports don't have to be squishy , and they should be killed last or not at all.
Mobility, CDR and team active items all day.
I would never build Athene's over Mikael's as a support.

Source: support main playing in Gold. I've done lots of research.
Favorite support: Sona

I play Nami/Sona main.

I usually have R-Sightstone, CDR Boots 2, Sight Wards, Shurelya's, Chalice/Athene's (for Sona only), Aegis/Bulwark (if jungler doesn't have it), and probably a Vision Ward. I hardly have enough money for a full build.