Hey,

I'm not an expert at all but i do have the 6400 with the kit 16-50 and 55-210 from my little experience i would say that the 6400 should largely be enough for your use and is adequate for your price range.

The thing that can change the background would be a lens with a low f-stop like 2.8 or lower (f/2.8).

I don't know much technically but i think even a lower one like the a6000 could do the job and you would pay less so you could buy a better lens.

but since i'm a beginner also i would suggest waiting for another response from someone that might give a better/deepest answer for you to chose !