I think Yamato's character is such that she's either:
1. Comparable to or weaker than Jack (if e.g. her main arc fight is against Jack)
2. Stronger than King (if e.g. her main arc fight is against Kaido).
The development of the Onigashima "arc" has seen me steadily shifting towards #2.
I'm starting to wonder if Yamato is the Oden of the Strawhat Pirates.
* Yamato is trying to be Oden.
* She'll join the Strawhats very late in their journey and accompany them for their final voyage.
* Like Oden she may be a Conqueror.
* Like Oden, she'll become Roger's 3rd strongest crew mate.
However, I don't really believe it. Oden was a Whitebeard Pirate that was on loan to Roger to help him on his final journey.
My thoughts on Yamato's Devil Fruit:
1. Byakko: it's thematic and fits her opposition to Kaido
2. Western Dragon: contrasts Kaido's Eastern Dragon and might fit her knowledge of dragons. Oda may also want to go for a less obvious choice for her DF.
I think #1 is more likely than #2, but those are the only options I think merit individual attention.