I have reorganized the list for the start of the 2017 racing season, hopefully making it a little easier to use, and updated a few things I know to have changed since 2016.
I should probably point out that some of those links for streaming may not necessarily work for every type of mobile device and/or streaming box.
After my old lap top finally gave up, I replaced it with a new mini-PC (just a small box, no screen or keyboard of its own) that sits permanently on a TV-stand shelf under my TV and is controlled with a remote keyboard. As far as I know most PCs I've seen easily connect to TVs with an HDMI cable.
Even though I no longer subscribe to their TV service, I still also have the Vmedia streaming box there too (I still use their internet), which I will sometimes use for streaming some of the things it can receive, usually when there's two or more live things happening at the same time and I can use the TV's picture-in-picture to simultaneously view both. I may have gotten one of the last TVs made with that feature, and I think you may now have to search Amazon or elsewhere to find an entirely separate box to provide picture-in-picture, though I guess most people today would rather use a mobile device to monitor a second thing instead of having them both on the same TV screen.
The Apple mobile device I have can also be connected to the TV in a similar manner with the correct adapter for the HDMI cable, (or of course also carried around a home with wi-fi), and I will add that my adapter has worked well when I've used it at home and at friends and relatives homes, despite all the complaints from reviewers on the Apple website. It seems to be capable of viewing some streams the Vmedia box can't, but not everything that the computer can.