As a matter of fact, this Linkstick should be compatible with the D6050.

-MrSamsung

From the available information, the BD-E6500 will indeed allow you to pass through content through HDMI INPUT 1 with out having to use the Player (there is a setting in the menu that will activate this feature, under the "System" sub-menu).

-MrSamsung

Unfortunately, I will not be able to tell you which TV is better, since all of the Samsung LCD and LED TVS will be able to display video games with the highest of quality. I would suggest looking for a TV that best fits what you are personally looking for in a device; with features, specifications and within the price range you are comfortable with. I will say that, traditionally, LED TVs are considered premium and therefore will more often then not offer better picture quality and more features.

Additionally, the UN55ES6100, like many of the other Samsung TVs, will offer a feature called Game Mode. Game Mode bypasses some of the TVs processors to give you an almost direct feed from your game system. This will help in the time it takes the signal to travel from the game system to the panel, effectively reducing the time between when you press your action button to when you see the action displayed on the screen, making for more accurate responses.

And finally, here is a quick synopsis of the differences between Samsung LCD and LED TVs:
LCD traditionally uses a CCFL (Cold Cathode Fluorescent Lamp) backlighting system that runs across the rear internal portion of the unit to illuminate the LCD panel from behind. This lamp technology enjoys a tremendous following of enthusiasts, and translates into years of enjoyment of an affirmed, reliable and trusted technology.

LED (in this application, it is also known as LCD-LED) is relatively new on the market, and uses specialized versions of the LED lights that have been used for years. It allows LCD panels to be lit either from behind (replacing the CCFLs with LEDs), or from the side using an efficient energy friendly infrastructure that emits light evenly behind the panel in order to illuminate the entire LCD panel equally, called EDGE-LED. EDGE-LED Technology has a few additional benefits in that the design of the LED panel can be slimmer than traditional LCD panels and reduces energy consumption.

LED also has a few additional benefits, such as offering an accurate and natural color, as well as increased performance with black levels. LED is also free from toxic materials, such as mercury, lead or volatile organic compounds.

-MrSamsung

Since the Linkstick is designed to only facilitate a network connection to Samsung Devices that already offer either network connectivity or Internet@TV and Samsung Apps, it will not have the ability to make the TV into a wireless monitor. (additionally, the Samsung TVs will not have the ability to directly process any Microsoft Office documents)

That said, there are three ways to connect your PC or Mac to your Samsung TV for monitor functionality: monitor cable, HDMI to HDMI or HDMI to VGA/DVI/Displayport.
Please note, in the PC's operating system, you will need to set the display settings to either clone or extended view and set the PC’s resolution to match that of the maximum resolution of the TV in order to view your PC's desktop on the TV.

Although all of these connections are easy to hook up, the PC monitor cable is the most common. To connect it this way, just use a standard PC monitor cable to connect from the monitor out of your PC to the PC input on the TV. Some adjustments to the PC's resolution is required.

If your PC offer HDMI out, I would highly suggest using this connection, since it is a basic plug-n-play connection (meaning almost no adjustment is needed on the TV or PC).

HDMI to VGA/DVI/Displayport is almost the same as straight HDMI, but in this case, you will want to connect the DVI end of the cable to the PC (if available) and the HDMI into the TV. This is also considered a plug-n-play connection.

Unless otherwise specified by your PC manufacturer, you will need to connect the PC's audio to the TV with a separate cable (3.5mm jack cable from the PC’s audio output to the TV’s DVI/HDMI Audio input), since most PCs do not support audio over HDMI, VGA or DVI.

Thank you for the opportunity to assist you,

-MrSamsung