I have not tried Vue yet, so there is not much input I can have there, but there are several like Vue to consider:
Sling TV
Hulu Live
Youtube Red
DirectTV Now
fuboTV
They are all worth comparing to see if
a) they have the channels you want at the price you want
b) they are available on your platform (Roku, Shield, Fire, etc...)
What is great about all of these is they offer free trials, and even after the trials, there is no commitment. You can sign up and cancel all willy-nilly as your needs change. Some offer free hardware for a minimum commitment.
ALSO, SOME channels have their own apps where you can watch their content for free (with commercials). Some require you to already have a cable or satellite subscription, but if you have a friend or relative that would be willing to provide you with login credentials, you can then activate these. History does have their own app, but I can not recall if it requires credentials.
Streaming out of market games is something else entirely. I have not done a lot of that, but it can be a frustrating experience. Yes, most people do these on a computer, and then you could run an HDMI cable to your TV.