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The a6000 is fine.
In new condition, with the 16-50mm f/3.5-5.6 kit lens, its listed on Amazon for 520€ incl. delivery.
Used, you can easily find it for around 300€, give or take. The kit lens is usually thrown in as "freebie." It isn't bad, but it has no other discernible use-case other than on the a6 line.
Menu is fine if you are coming into it new, if you have nothing else to really compare it to. LCD is functional, and can swing out upwards or downwards a little, not side-to-side. You will want to use some savings on a few better lenses. Sigma offers a few nice primes, and I hear Yongnuo has some cheaper options as well.
If you really want something on the a6 line, get the a6300 or a6500. They're better for video capture than the a6000.
The a6400 (and even newer a6600) is still rather new-ish, and over your budget.
>tl;dr - can you do better than the a6000? Sure, but if your budget can't, then its perfect.
