Admirals, purely because I rarely build harbours or even near-coastal cities before the modern era. Also the fact that I only ever see 1-2 admirals claimed in a whole game by the AI, I have no idea if there are even any good ones. All I see are the ancient, standard ones.
Writers soon enough. With an amphitheater in every city, and almost every single wonder that gives writing slots, I 100% am always ending up passing on dozens of these over the course of the late game, with nowhere to put them.
Even my art museums will get full soon enough. So I never bother 'going for' any cultural people.
Scientists, merchants and industrialists are the only ones I go for. And even then, only the ones that add to space projects, add to wonder construction, or give me new amenities, or +housing and +amenity in that city.
I quite like the occasional great general. By mid game I have a fair few encampments and get a lot of GG points. Some of them are helpful if you're turtling and have neglected an army. The one that gives a free bombardier unit, which you can get really early. I remember getting that the first time in like 500bc. I could 2 shot cities with walls and take them with a scout. Was too powerful. Or ones that make a unit an army.
So frankly I find myself passing on most great people