Yeah it's really a matter of figuring what you want out of them and then doing what makes sense.
At launch, I ran a bunch of different NPCs for virtue pots for rapport. Elia, Ryeon's ghost, Azena(up to amicable which is really early) for example. I also made sure to pick some early NPCs since I figured I wanted to do the rapport stuff everyday easily without needing to clear x island or have y stat, so I was also doing Seria in Prideholme for the adventure tome item and Thunder for the same reason. I also started right away on Beatrice rapport even though I could only do one emote and one song due to not having the others unlocked. As I finished some of these or dropped others(Thunder, I also had Thirain in my initial rotation for gold but never got far enough), I switched to other stuff. Beatrice 2songs/2emotes once I unlocked them until I got her heart last week, Blackfang 2songs/2emotes to work towards Astray as I was also doing the una task(not done with that by I'm almost at friendly without having gifted her anything yet for ex so that'll save me a bunch of gifts to get the Astray) and then a mix of stuff. Once I got to T3 I switched the mix to Punika NPCs, Nia 2songs+1emote and I did the remaining emote on the NPC next to her(low req NPC for adventure tome completion). Since I finished Beatrice, I moved her stuff to more Punika, I do Nia, 1song 1emote on that NPC next to Nia and 1song 1emote on the fox and 1 emote(the leftover since Nia has only 1 emote but 2 songs) on Liru. Rest blackfang but once I finish blackfang(probably today), I'll move her stuff to Punika too.
Ultimately you don't unlock all that much from the free rapport shit though, just make sure you use them towards NPCs that have interesting stuff but a lot of rapport unlocks have to be done with gifts. I was doing some calvasus for a while for giant heart but just dumped gifts on him to unlock it asap once I had enough for 10(with 12 being beatrice+tooki which ended at aorund the same time last week).
Una rep was a bit more complicated because I also tried to balance out daily rewards efficiently between chars, so most alts had at least one leapstone or shard reward(and once I had more room to work with, 1 of each). I focused heavily on long term grinds(Astray, Eibern's Wound for ghost ship weekly, Tooki for giant heart, Azure Wind for giant's heart, Whispering Islet for skill pot, Punika 21days for omnium star, Rohendel 7days for skill pot) and then on getting all the virtue pots(only 2 left from the more annoying shit). Now my current Una tasks are focused on unlocking vendors and food items for adventure tomes and the last 2 remaining virtue pots but I have finished most of the grinds.