Certainly not the 35mm. It is too wide to be a main lens for people shots, even infants. For an occasional baby shot, yes, but you will quickly tire of that as your only perspective. You'll get comments "These are nice, but they look a little weird. Are you too close?"
55mm is ok and usable as an only lens. For decades this was the FF focal length that all cameras came with and for good reason.
Personally I'd recommend, if you can, the kit zoom and a prime. A zoom gives you a lot of "fall back" flexibility that I think is important.
If getting the kit lens and the 55mm is a budget buster for you, I might get the A6000 instead, but if you have your heart set on upgrade to FF, then you'll be a little constrained at first.
I shoot mostly young children and toddlers. For a prime as an addition to the kit zoom, I'd consider the 55mm and the new 90mm, but I'd probably go with the 55mm. Opinions vary of course about "portrait length" (I prefer 75mm f2 for children indoors), but only if my indoor spaces were very large and very well lit would I consider the 90mm for shooting informal portraits of children engaged in normal activities. The longer focal length amplifies the tracking burden on you of their movement and without very bright light you'd be shooting wide open all time, which is not the best. BTW they go from infant to zipping toddler much faster than lenses get old.