I always go for the Happy Ending first, preferably with a guide in hand.
For me, the Happy Ending feels like the 王道, or the standard/classic conclusion of the route. It's usually where everything comes together: the relationship reaches its proper resolution, unanswered questions are revealed, conflicts are resolved, and you finally get the full picture of the story.
With Bad Endings, on the other hand, you often don't get all of that context. Of course, it depends on the game, but sometimes if you play a Bad Ending first, you won't fully understand the meaning behind it or be able to read between the lines because you haven't experienced the complete route yet. There might be certain details or emotional implications that only make sense after you've seen how things were supposed to unfold.
That said, I do enjoy checking out Bad Endings afterward, especially when they get dark, dramatic, or unexpectedly spicy. Some games have Bad Endings that go in directions the Happy Ending never would, like the heroine ending up with someone else instead of the LI of that route, or other wild scenarios.
But that's exactly why I prefer to save them for later. I want the Happy Ending to be my main experience and emotional conclusion for the route first. Then, once I'm satisfied and emotionally secure that everything worked out in the end, I can go back and enjoy all the alternative disasters as bonus content.