Price: can only speak from where I live, but it seems from your comment that it is alittle over budget.
Screen size: 43, 50, 55
Resolution: full hd
SmartTv: Yes, android, nuff said?
Refresh rate: 100Hz with 800Hz motionflow
Response time: 10-15 ms (Do not have any source on this, but this is stated from Sony who visited our store.)
VESA mount: Yes
3D: yes, active, no glasses included.
I would not recommend 4k, because 4k is useless without HDR, and there is no HDR standard today, which means that if the state a standard, and you television do not support the standard, again it will be useless. So even I you buy a 4k tv with HDR you might not be able get the full experience with 4k.
From what I have learned Sony has the best response time 10-15 ms on their flagships, LG around 30 ms and Samsung 45-50 ms. Please see if you can find a source on this. The Sony w807c has Sonys "finest" display, the Triluminos display. This means that it will show a good picture when viewing from the angels, please see link provided.
DLNA server which is Mezzmo
I am unsure of this, but it runs android smart tv so if anyone should support it, I would be android.
Since it is android smart tv you can use the ps4 control to play games from google play, and aswell control the tv with it.
THe tv has a built in google cast, which means that you can cast you smartphone directly to the tv.