I think you need a Roku device for every TV. I have a Roku desktop, about 4x4x1, and a Roku stick which plugs directly into the TV. The desktop Roku is better.
You’ll need a fairly high speed internet connection for good Roku service, say 20Mbps. Even so, there is at times some splotches that come and goes. Usually this is when you’re watching a football game or something and there are 10 zillion others watching.
Some of the streaming channels allow you to record live shows and watch them later. Usually, these are not cheap though.
I would echo the Roku suggestion. We dropped cable a while back and went with Roku on all three TV’s . Don’t need to record a’tall since the Roku channels keep the same series/movie for watching for a very long time. If you watch it part way early in the week and want to finish it later, just go back in and restart.
However, you will start spending more if you subscribe to all the channels: Netflix, Hulu, Amazon, Britbox, etc. Their monthly charges will accumulate. However, you can sign up on a monthly basis, watch what you want, and drop them. Their contracts are not restrictive like what cable companies insist on. Another however, you will need a good internet connection (~20mbs). I use AT&T’s and have been happy for years.