I have both a D300s, and a D600 that I got a week ago.
I would agree that the D300s feels a little more solid. But I think the D600 is solid enough.
I have only done two photoshoots, with the D600, both in tough circumstances. The first was shooting a private karate lesson for my son in a barely lit room. I shot with the 50mm f1.8. The results wee superb at 3200 and impressive at 6400.
The second was a high school basketball game. Other than some concerns about if the AFC tracking was locked on, I loved it. I shot with a 85mm f1.8 and the shots had a wow factor that I never had with the D300s.
(I do not post pictures of karate or hs basketball in forums, all of these kids are under 18.)
I have fooled around with the kit lens a bit, and I think it will be very useful. I see vignetting, and barrel distortion and pincushion distortion. The first problem can be dealt with by stopping down to f 5.6, and you have the ISO headroom in the camera and the VR in the lens to do it. Both distortions can be dealt with in post processing. Other than that, I think is the lens is fine and is getting the "kit lens" bad rap...
I passed on the 70-300. That is a lens that I think is outclassed by several options.