So, for the Fire type since people seem to be convinced that they are based off the chinese calendar (while I'm not that shure since Fennekin is a Fox and not a Dog and Cyndaquill isn't neither a Rabbit or a Mouse...)

http://www.greenberg-art.com/.Illustrations/.Serious/qq1sgChineseCalendar.jpg
I think a Tiger would be really badass, but I'm also interested in seeing what they could do with a Sheep (probably Fire/Fairy) or a Horse which might give us the long awaited Fire Pegasus (saddly overshadowing Rapidash but hey, he got his chance to evolve in the past 5 gens excluding 5th)
So:
1- Since we're talking about Sun and Moon I expect the grass type to be higly focused on photosyntesis, it might also get a better version of Clorophyl but that is disadvantageous in case that there is any other weather condition, something like 1.5 atk 1.5 speed under the sun and 0.5 speed under any other weather condition. I don't have any particular idea but I'd like a mon based off either Bamboo or Palm Trees (hint hint Hawaii), please no flowers, Meganium is a thing and everybody hates it...
2- Tiger, Fire/Electric or Fire/Dark ;
3- Dolphin (it'll never happen) random fish that becomes Water/Dragon (Dragon would make electric 1x against the Pokémon, letting a possible Fire/Electric starter not beeing OP) .