You’re spot on about the three tunings (honchoushi, niagari, and sansagari). Interestingly in the name of the tuning itself it hints at the intervals used (honchoushi meaning “origin tune,” as it’s the base of the other two, “niagari” meaning “two raised” since the second string is raised from honchoushi, and sansagari meaning “third lowered” since the third string is lowered from honchoushi). I’ll do my best to answer, but please keep in mind this is from a completely Tsugaru point of view (it seems a bit like the frequency of what tunings are used are regionally specific to some extent), as my knowledge on other regions’ folk music as well stuff like nagauta/jiuta/hauta/kouta etc. is very limited. Please excuse the wall of text and enjoy
The majority of the Tsugaru repertoire I’d say is niagari (in your example, DAD) with three of the Godai Minyo (the “big five” folk songs, Jongara Bushi, Aiya Bushi and Yosare Bushi being niagari) as well as plenty of the general standards in the genre (such as Tsugaru Jinku, Ringo Bushi, Kuroishi Yosare Bushi, to name a few common ones). Niagari also is by far the most popular for modern compositions.
Honchoushi (DGD in your example) is still pretty common, being used for one of the godai songs (Ohara Bushi) and still a fair amount of folk music (Ajigasawa Jinku is probably the go to here for 100% Tsugaru songs but not Godai songs in honchoushi, or Akita Nikata Bushi which isn’t from Tsugaru itself but was sort of adopted into the repertoire) but it’s used less often that niagari in Tsugaru. Akita Nikata Bushi and Nanbu Nikata Bushi are a couple examples from the general region (though not specifically Tsugaru) that uses this tuning. Soran Bushi is pretty popular, and is a honchoushi song from Hokkaido. But Ohara Bushi is really the one I’d say people think of for this tuning. It seems really common in Akita songs, for whatever reason, or at least the ones I know.
Sansagari (DGC in your example) is pretty uncommon, compared to the other two. It’s used of course in the piece Tsugaru Sansagari, as you might’ve guessed
It’s also used in a few other Tsugaru folk songs, such as a popular arrangement of Yasaburo Bushi or with Tsugaru Ondo, but there are fewer songs in general in this tuning. It’s common for the title of the song itself to denote if it’s in Sansagari when it is used, such as in the cases of Tsugaru Sansagari and Nanbu Umakata Sansagari, which attests to the fact that it’s not used very often since it’s considered the defining feature of those pieces.
Of these I feel that Niagari gives me the most versatility, and has the most quintessentially “Tsugaru-esque” sound of the three, probably due to its frequency being used.
But, all three are considered standard to use. It doesn’t matter what key a shamisen’s necessarily in so as long as it’s in tune with itself, so don’t worry about getting it DAD, for example, since CGC or AEA for example all are good for niagari. The same conventions go for honchoushi and sansagari as well - it doesn’t matter really what key you’re in for any of them, since you would match a singer’s voice or just play whatever sounds good to your ear. Of course with modern pieces people often set a key, but that’s another story, since I’m really just talking about traditional pieces here.
C as your bottom note (since the other two would be tuned relative to it depending on which tuning you’re using) seems to be one of the more common tunings and I believe is the one recommended on the tunings page here, since it’s not really too high or to low. But you can choose whatever suits your ear, really.
Today’s aesthetic goes for a very bright sound in contrast with the warmer sound of the older players, like Christopher said, but like he also said, do whatever suits you.
Hope this helps!