Get a sony KDL 50R550A or if you can't find one at the right price like I did, go for a 50R450A. They are a beautiful set, the 550 being of better quality but pricier. Getting a Sony TV direct from sony with a sexy frame, many extra features

http://store.sony.com/50-diag-r450-series-led-hdtv-zid27-KDL50R450A/cat-27-catid-EOL-Sony-HDTVs

http://store.sony.com/50-diag-r550a-series-led-internet-tv-zid27-KDL50R550A/cat-27-catid-EOL-Sony-HDTVs;pgid=cNR8cDctSERSRpCUFKtaSFQ.0000jit1dT0F?_t=pfm%3Dsearch%26SearchTerm%3D50r550

Others to take a look at

http://store.sony.com/47.6-diag-w600b-series-led-hdtv-zid27-KDL48W600B/cat-27-catid-Sony-HD-TVs

http://store.sony.com/47.6-diag-w600b-series-led-hdtv-zid27-KDL48W600B/cat-27-catid-Sony-HD-TVs

http://store.sony.com/40-diag-w600b-series-led-hdtv-zid27-KDL40W600B/cat-27-catid-Sony-HD-TVs

http://www.bestbuy.com/site/sharp-50-class-49-1-2-diag--led-1080p-120hz-hdtv/5420114.p?id=1219128177728&skuId=5420114&st=categoryid$abcat0101001&cp=1&lp=2

edit - 

IDK if this helps but you can try game mode, there's a manual to your tv on their support page - http://www.samsung.com/uk/support/model/UE46F5000AKXXU

Game Mode is a setting used to bypass different operations in the TV. When Game Mode is enabled one of the major changes is the DNIe chip in the TV is bypassed. Bypassing the DNIe chip disables some video processing in the TV, which in turn allows for a faster video response time. This is useful when viewing a fast-paced video source such as a video game.

With your TV powered on press the MENU button to open the Main Menu.

1. Use the navigation pad to select the System menu and then press ENTER.

   

2. Use the navigation pad to select the General section of the System menu and then press ENTER.

   

3. Use the navigation pad to select ON for the Game Mode option and then press ENTER.

   

4. Press the BACK/EXIT button to leave the menu.

NOTE

● Precautions and limitations for game mode

– To disconnect the game console and connect another external device, set Game Mode to Off in the setup menu.

– If you display the TV menu in Game Mode, the screen shakes slightly.

● Game Mode is not available in TV mode.

● After connecting the game console, set Game Mode to On. 

Unfortunately, you may notice reduced picture quality.

● If Game Mode is On:

– Picture Mode is set to Standard and Sound Mode is set to Movie.

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on the topic of 4k sets

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If I was considering getting a new 4k set for less then I would look into the Vizio P series.  

It's an entry level 4k set that starts at $999 for the 50" and has some good reviews so far.

I would check out any set in person, and if you live in the US then wait for Black Friday deals.

http://www.theverge.com/2014/9/23/6832447/vizio-p-series-4k-tv-release-date-pricing <-- general preview

http://www.rtings.com/reviews/tv/lcd-led/vizio/p-series <-- in depth review

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edit- if you don't live in the US the Vizio P set might not be available to you

and if you're looking for a tv that is 1080p and mostly used for gaming then the above Sony sets are better

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Get this Optoma GT1080ST $749. Its a short throw projector so you can project a 100" with the projector under 4ft from the wall. You can mount it on your ceiling or just put it on a table .

And then with that you can do this

Trust me... once you go with Projectors.. you can never go back. 

I'm not so sure about the advice to get 4k TVs.  Upscaling of computer generated content like games is rarely great.  It will be a lot more expensive, and games will look worse than a native 1080p TV.

B-But capitalism!

Agreed, but you're opening a whole new can of worms to research.

That projector has a lamp life of 5000 hours, so check first how much replacement lamps cost and whether the lamps deteriorate during the life cycle. Not all lamps last the estimated duration, although some can last a lot longer too, kinda luck of the draw. Don't foget the cost of a screen and sound system. Plus check first if you're not sensitive to the DLP rainbow effect.

http://www.projectorcentral.com/Optoma-GT1080.htm
It's recommended for gaming, however it doesn't have lens shift nor optical zoom so you're a bit limited with placement.

4k becoming the norm? Aren't most broadcast tv shows on major networks (CBS, Fox, NBC, Sports, etc) all in NATIVE 720p still?

Less then 600 bucks best tv for gaming

https://www.google.com/search?q=samsung+plasma&client=ms-android-sprint-us&espvd=1&source=lnms&tbm=shop&sboxchip=Shopping&sa=X&ei=lq1EVKKnL4-WigKux4GIBQ&ved=0CAYQ_AUoAQ#spd=2626722328414415063