I've been working through this exact question myself. I tend to have a clusters of colors that I really like.
Teal/Blue+green: Yama-dori (Sailor), Syo-ro (Iroshizuku). Honorable mention goes to Columbine Blue (DeAtrementis). If I had to pick one it would probably be Syo-ro, but the fight with Yama-dori would be a tough and bitter one.
Red/Burgundy: Edison/Red-Black(DeAtrementis), Oku-Yama (Sailor), and Yama-budo (Iroshizuku) when I'm feeling perky. I've recently acquired a bottle of Irori (Sailor) and I'm still figuring out how I feel about it. If I had to pick only one it would be Oku-yama, but I would be sad and cry for my Edison.
Greenish. I love the murk. Love the swamp. Love the ambivalence. Sailor Rikyu-Cha is one of the most drop-dead gorgeous inks on the planet. It is the only ink that I horde because I can't imagine an acceptable substitute. Honorable mention goes to Ina-ho. No, I don't know what color it is. But when the mood hits it is the only one that will do.
Purple: Poissere De Lune (J. Herbin), Shigure (Sailor). I love purple, but I am still searching for purple ink perfection. I love and regularly use both of these, but the Herbin is just a hair too red for perfection and the Sailor is a hair too blue and too dark (I use it as stealth blue-black at work). There have been many purples that I should have liked but were too... much. Too bright. Or too light. I have to get some more samples. I've been working through some purple greys, which has turned out to be a category that I enjoy very much but isn't the same as a proper purple.
Brown: Lie de the (Herbin). Honey (KWZ). Very different browns, but both beyond lovely. I'm not sure I could pick one over the other. Honorable mention: Doyou (Sailor). It is a stealth black, but manages to be more interesting than black. I got it in case I ever have a demonstrator staining incident, so I don't actually use it much except for work. It's a nice ink, though.
Blue-black: Tsuki-yo (Iroshizuku), Sei-boku (Sailor), Yonaga (Sailor) is a new one to me that I've come to like much more than I expected. Honorable mention goes to Pilot Blue-black, which is boring in all the best ways. Sei-boku is permanent while still being well behaved and a good color.
Grey: Lexington Grey (Noodlers), Chu-shu (Sailor). These have very different shades. Lexington Grey looks almost like a pencil, but is completely permanent. Chu-shu has a hint of purple.
The other groups I use more for than completeness than because they float my boat. Many of them (noted) are work inks. Work inks have to pass for blue or black and look as un-appalling (that might not have been a word a few minutes ago, but it is now) as possible on green, blue, yellow and pink copy paper (don't ask). I do use all of the blue blacks listed above at work.
Blue: While I love blues in life, I'm not a particular fan in ink. I tend to find them too bright or too anemic. I've not found a happy medium. I use Horizon Blue (Monteverde) and Souten (Sailor) on white or blue paper at work from time to time. They're horrible on the rest of the color-coded note paper. Visconti blue is also fine.
Actually green: Miruai (Sailor). Tokawa-matsu (Sailor). I could live without a proper green green and be totally content with my lot in life, but these are the best greens I've found. I use Miruai at work as a stealth black (dark enough to hide on all the appalling colored paper). I've got to get another sample of R&K Alt-goldgrun because I remember really liking that one, but I ran out my sample and never re-bought it because it's green, and I'm not a big fan of green. There were always more important colors on my list. Honorable mention: Lierre Sauvage (J. Herbin). This is about as middle of the road green as you can get. My son loves it, which is why I keep buying it. It is also well-behaved and... green. So if I need a just green green for editing or some such and the Tokawa-matsu is not available or appropriate for some reason (I can't imagine why that would happen, but this is theoretical) this is my green.
Black: work only. Life is too short for black ink. But with that said, it's Sailor Kiwa-guro all the way. The way that ink feels in a pen almost makes up for the fact that it is black. Almost. The water-proof factor is also nice. Honorable mention goes to Heart of Darkness (Noodlers).
edited for typos
Edited by displacermoose, 07 September 2018 - 03:41.