Which is the the best 4K TV monitor around 50 inches for the Mac Mini 2014 (3 GHz, I7, 16GB RAM)?

Best is too subjective to give a good answer. Not that the 2104 Mac Mini can only support 30 Hz at 4K.

• Support for 1080p resolution at up to 60Hz
• Support for 3840-by-2160 resolution at 30Hz
• Support for 4096-by-2160 resolution at 24Hz

Some users find 30 Hz unacceptable

What Samsung display o y now have and how is it connected?

Users seem to get better picture if the display has a displayport or mini display port input vice HDMI

I have used my MacBook Pro Retina with myVIZIO P502ui-B1 4k and was pleasently suprised with the quality. If I had a Mac Mini I would definately recommend it as a monitor. I hope the next gen Apple TV supports 4k airplay mirroring!

I have heard somewhere that there have been problems between apple products and Samsungs TVs in the past.

I have experienced the same. When using Apple products try to avoid Google, Samsung, and Sony. Although, the real culprit may be the Hollywood cartel, they have multiple copy protection schemes that can interfere with legitimate customers.

There are two possible interfaces by which you can connect a 4K display to a Mac, one is Displayport and the other is HDMI, however HDMI 1.4a only supports 4K at a maximum of 30fps, to get 4K at 60fps you would need HDMI 2.0. Unfortunately no Mac ever made so far - including the 'new' Mac Pro supports HDMI 2.0. Adding support for HDMI 2.0 requires a video card that supports it so no current Macs can be upgraded to HDMI 2.0 either.

Note: While in theory a 'classic' Mac Pro can be fitted with a GTX 980 card which does have a HDMI 2.0 port this is not supported (yet) under OS X, it only runs at HDMI 1.4a mode.

Displayport 1.2 which is supported by current Macs can do 4K at 60fps, however there is a grand total of one TV make in the entire world which supports Displayport, all other 4K TVs use only HDMI 2.0. See http://www.panasonic.com/uk/consumer/viera-televisions/led/tx-l65wt600b.html

As a reminder, the latest Mac mini has Mini Displayport 1.2 and HDMI 1.4a interfaces and as Illaass says can do a maximum of 4K at 30fps. The previous Mac mini does not officially support 4K at all. Since the Mac mini can only do a maximum of 30fps it might be considered an inadequate choice from a 4K point of view, a Mac Pro, or MacBook Pro Retina would be alternative but more expensive choices which do support 4K at 60fps.

There are numerous 4K computer displays which will support using Displayport and remember Mini Displayport is 100% compatible with Displayport it is just a different type of cable/connector. As Illaass again says best is a subjective choice. Some criteria to consider include the following.

• Computer gamers are often concerned about getting a display with the fastest possible refresh rate, it happens that TN type screens (Twisted Nemetic) have a faster refresh than IPS screens (In Plane Switching), refresh in this case is not exactly the same thing as frames per second, however it does also mean that some TN screens can even do 120 or more frames per second (at less than 4K resolution). IPS screens have better colour accuracy, better viewing from an angle and various other superiorities over TN screens. Apple's own screens are all IPS
• Related to the above TN 4K screens are likely to be cheaper than IPS 4K screens
• Some 4K screens can do 4K at 60fps via SST (Single Stream Transport), some require using MST (Multi Stream Transport), OS X is very poor at supporting MST so getting a screen which supports 4K at 60fps via SST would be an advantage
• Not really related to 4K but Apple still do not support 10bit colour depths so buying a screen purely on this criteria would be a waste of time and money

In theory an active Displayport (or Mini Displayport) to HDMI 2.0 adapter is possible, currently no such adapter exists but several articles suggest these might become available this summer. This would then let you use the Mini Displayport interface on a Mac and connect to a 4K TV which uses only HDMI 2.0.

There are some so called Mini Displayport to HDMI adapters already on the market claiming 4K support but these use HDMI 1.4a and are limited to a maximum of 30fps at 4K. There are some dodgy Amazon market place resellers conning people over this - check the reviews.