Honestly OP, I think pretty much any 1080p TV will make you happy so I say shop by price and stick to a reputable brand. Forget about the other specs because you're not going to notice them. The only specs I might recommend are a 120+ Hz refresh rate and LED backlight. Not because they're necessarily all that superior but because those things are pretty standard nowadays so you might as well keep with the times.
My recommendation is Vizio. They started out as a budget, no-name TV set and now they're competing with the major brands. At the high-end the big names will likely still win in a comparison test. But for anything less than top-end I think Vizio is the best bang for buck. Save some money on the name and either pocket it or put it towards a larger screen size or feature set.
I'm actually a little stunned that this isn't already built in to TVs already with NFC or Bluetooth or some other magic power I have never used. I had a Nokia phone about 4 years ago that could Bluetooth to a monitor. Because Symbian OS screens are more exciting on monitors than on the phone I guess?
I'm very behind but I thought the future was further ahead.
Still waiting for my Mr. Fusion Delorean adapter to show up as well.
EDIT: this just rang a bell. Damn the thing is $215. How is it different from a Chromecast for $40?
Actually, there is a screen mirroring service built into some TVs. It's called Miracast but it's often re-branded by the TV manufacturer. For example, Samsung calls it "AllShare Cast", LG calls it "Smart Share" and Sony just calls it "Screen Mirroring". Miracast is baked into Android natively as well Windows 8.1 and Windows 10. So, in theory you if you're running any of these operating systems on your computer/device AND your TV supports Miracast then you can wirelessly mirror your device to your TV screen.
Chromecast is a different animal. It doesn't do screen mirroring. It's actually more like a set-top box that streams content from the Internet. It also syncs with your device (computer or phone) which allows you to pause the video you were watching on your phone and continue watching it on the TV. You can also use your phone/computer as a remote. This gives the illusion that it's mirroring your screen but it's really not. It's only compatible with certain services (like youtube, Netflix, etc).
Get a tv with 4k. 1080p is out. Quick refresh rate for action
Personally I'd say avoid 4K for now. When people ask me why these are the reasons I give:
1. Lack of 4K content available
2. Price
3. Not much point unless you have a pretty large TV or sit very close to the screen
4. Some lower priced sets operate at a lower refresh rate at 4K resolution
5. Wait to see if 8K supplants 4K as the next ultra HD standard (hey, it happened with 720 vs 1080)
That being said, if you just want one so you can geek out over it that's totally cool too. I would if I had the money to burn.