Putting a culture center on a dead-end planet is a bad idea. It's more efficient to put one on a planet where routes have at least 2 phase lanes to go in whatever direction: that is, a single culture center at "My Home" would work, or putting one (preferably) on "Planet One" would work. You probably shouldn't be building more than one or at the most two culture centers if at all possible: logistics slots are precious, and every unnecessary culture center you build means 2 fewer credits per second you'd get from a trade port that could have been there.

What I generally do is I only build one culture center, on my front-line planet, which will eventually increase the culture to maximum in the back of my empire, but will also fight off enemy culture coming my way.

Culture stations are kind of like taps with water flowing through them, and phase gates are channels through which the water passes.

I think having one or probably 2 frigate factories on your front-line world would be essential.

But even if you try to max out on logistics slots on that front-line world, I don't think it's viable to build more than a single culture station there unless the world is still being completely overwhelmed by culture - any halfway decent opponent will easily negate whatever cultural aggression you attempt, for a lower price (it takes a lot less to defend with culture than to attack with it). Capital ships easily suppress enemy culture from advancing.

The additional income that trade ports would give you or the additional utility that one or two frigate factories would give you would be worth much more than the investment into maxing out on culture centers that you say you often do.