Satellite broadband is horribly expensive. Not unlimited, either. I had it for a long time, with very poor customer service and support if there was a problem, and there were lots of problems. I think the limit was 12 GB per month. Can't get DSL or any kind of copper-based internet. For a while I had Verizon's "LTE Installed" cantenna, which was a better deal but still limited to about 18 GB for all the devices in the house (two computers, phone, ipads). Now I have a Verizon Jetpack which comes with a 15 GB allotment I use for the computers and tablets. I have another 15 GB hotspot data on my phone I can use. I know it isn't enough to stream 4K, or even much HD video. But it would be nice to watch a few things that aren't on the DirectTV channels, like John Oliver's show or a couple Amazon Prime videos.
I looked into getting the Lightning-HDMI cable. Most advice seems to say pony up for the expensive one from Apple because with any software update they could make third party cables non-functional. That started me looking at Apple TV, since I could use AirPlay to stream to that. Apple support told me today that as long as the TV has 4K and HD, it should work with 4K Apple TV and the quality of the video will depend on the resolution of the Apple TV box. So if I'm streaming an HD movie from Amazon Prime, using AirPlay to cast to the Apple TV, the video will be HD quality on the screen.
Since the Apple TV is near the end of the life cycle, I think I will go ahead and get the lightning-HDMI cable from Apple and use that for now. Advantage is I can take it with me when traveling. I hesitate because I read that the video from the cable would be like a giant blurry iPhone screen, but I think if I have a direct connection and am not using screen mirroring the video will be ok. I'll go to the Apple store tomorrow to ask about it before i buy one.