If you want to broadcast your game play over the internet, take a look at Justin.tv (http://www.justin.tv). Unfortunately I haven't hosted any live gaming sessions on it, but I watch a lot of games using the site. The game play appears smooth and does not display any lag.
This video shows how to set up your computer for broadcasting WoW.
A lot of people use it so I think it would be a good choice.
If you only want to share your desktop on a LAN, this might not be suitable.
OK, I'm going to set the record straight here since I know quite a bit about this topic. ;)
Modern advertising has confused the masses in regards to Hz.. so here it goes.
All consumer grade HDTVs (that I have seen so far) do not accept greater than a 60HZ input - meaning - that 60fps is the highest framerate you can achieve on a modern HDTV with vSync enabled.
Now that we have that straight.....
Where things get tricky/confusing is when manufacturers advertise 120HZ, 240HZ, 480HZ, etc.
The input signal is still 60HZ. (blu ray movies technically run at 24hz, but we're not talking about that) Notice that each of those defined HZ above are multiples of 60HZ.
What's really happening is this: HDTV manufacturers have engineered software that interpolates motion. Motion interpolation software takes information from frame A, and frame B, and averages the brightness and color coordinates in each frame to create a third frame between the two.
Middle frames are new. They were never recorded as part of the original content.
This makes the picture look very smooth, but is BAD for gaming as it's causes input lag and response lag.
So to answer your question, 60HZ is best for gaming.
What's more important for gaming is your pixel response time, which you can check for several TVs here: http://www.displaylag.com/display-database/
Also, you might try connecting to the HDMI (DVI) port on your TV.
Head over to http://www.displaylag.com/display-database/ and set your filters to the following:
Set the size to the screen size you'd like to have and start checking prices. (it will link directly to Amazon) You want to pick a TV that has a Great or Excellent rating.
If the prices are still above $950 then drop down to the next smallest screen size and check prices again.
Keep repeating this process until you find a TV with a Great or Excellent rating that is $950 or under.
Good luck!
Best Answer
Streaming from an Xbox One to a Windows 10 PC will be heavily dependant on the quality of your local network, whether that be via ethernet or WiFi, and the quality of the experience will be largely down to latency.
The latency and quality of signal when using WiFi is dependant on the environment - that is, quality of walls, other WiFi networks in the same area, etc, so if you're having issues it might be worth re-testing with a wired connection.